Evaluate. Write your answer as a fraction or whole number without exponents.

6^–3 =

In 1970, an industrial waste site contained an estimated 350 tons of contaminated soil. special cleaning crews were contracted to clean up the site. the crews can remove 20% of the contaminated soil each year. describes an exponential function because it follows a fixed rate of decay over time, which can be expressed as a mathematical formula.

The given data describes an exponential function because it describes a quantity that decreases at a fixed rate over time.

The 350 tons of contaminated soil represents the initial quantity, and the special cleaning crews removing 20% of the contaminated soil each year represents the rate of decay. This decay rate can be expressed as a percentage decrease, which describes an exponential function.
To be more specific, an exponential function is a mathematical model that describes the decay of a quantity over a period of time. The decay rate can be expressed as a constant, which is multiplied by the initial quantity. The resulting value represents the quantity of the item at the end of each time period.
For example, in the given situation, the initial quantity of contaminated soil is 350 tons.

After one year, the quantity decreases by 20%, or 0.2, to represent the amount of contaminated soil removed.

This can be expressed as a mathematical formula as follows:

Q1 = 350 x 0.2

where Q1 is the quantity after the first year.

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Answer:

Step-by-step explanation:

We can start by simplifying the expression using the laws of exponents:

343^(2x) * 49^(-x/2) = 49^(x/2)

We can then simplify further by expressing everything in terms of 7 (since 7 is the common factor of both 343 and 49):

(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)

Applying the laws of exponents again, we get:

7^(6x) * 7^(-x) = 7^x

7^(6x - x) = 7^x

7^(5x) = 7^x

Now we can solve for x by equating the exponents on both sides:

5x = x

4x = 0

x = 0

Therefore, the solution to the equation is x = 0.

Answer:

x = 0

Step-by-step explanation:

343^(2x) * 49^(-x/2) = 49^(x/2)

(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)

7^(6x) * 7^(-x) = 7^(x)

Now, we can simplify the equation further by combining the like terms on both sides:

7^(6x - x) = 7^(x)

7^(5x) = 7^(x)

We can solve for x by equating the exponents on both sides of the equation:

5x = x

4x = 0

x = 0

Therefore, the solution to the equation is x = 0.

The volume of the cone in terms of π is option (c) 100π in^3

The formula for the volume of a cone is given by:

V = (1/3)πr^2h

where r is the radius of the base of the cone, h is the height of the cone.

In this case, we are given that the radius of the cone is 5 in and the slant height is 13 in. We can use the Pythagorean theorem to find the height of the cone:

h^2 = y^2 - r^2

h^2 = 13^2 - 5^2

h^2 = 144

h = 12 in

Therefore, the volume of the cone is:

V = (1/3)πr^2h

V = (1/3)π(5^2)(12)

V = (1/3)π(25)(12)

V = (1/3)(300π)

V = 100π cubic inches

Therefore, the correct option is (c) 100π in^3

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Answer: 100π in3

Step-by-step explanation:

Answer:

We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.

The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:

Four months: balance = $630

Six months: balance = $520

The change in the balance over the two-month period is:

$520 - $630 = -$110

The slope of the line is the rate of change of the balance per month, which is:

slope = Δy/Δt = (-$110)/(6-4) = -$55/month

Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:

y - 630 = -$55(t - 4)

y - 630 = -$55t + 220

y = -$55t + 850

Therefore, the equation that models the balance y after t months is:

y = -$55t + 850.

Answer:

Step-by-step explanation:

The solution (16, 2) means 16 small gloves and 2 large gloves can be made in less than or equal to 16 hours and cost less than or equal to $40 in materials to make.

Answer:

Sure, I can help you solve these problems using substitution. Let's start with problem 1:1. y=x+4 y=3x To solve this system of equations, we need to substitute one of the variables from one equation into the other equation. We can solve the second equation for y:y=3x Now we can substitute this expression for y into the first equation:y=x+4 3x=x+42x=4x=2 Now we can substitute this value for x into either equation to solve for y:y=x+4 y=2+4y=6 So the solution to this system of equations is x=2, y=6. You can follow the same procedure to solve the rest of the problems. 2. x=-2y+1 x-y=-53. y=x-7 2x+y=84. y=3x-6 -3x+y=-65. x+2y=200 x=y+506. 4x+3y=1 x=1-y Let me know if you need any further assistance.

The function is increasing over the intervals D. -6 < x < -1 and 2 < x < 3 and 4 < x < 6.

A function is increasing when the slope of its graph is positive, meaning that its graph is rising from left to right.

In the given coordinate plane, the graph of the function consists of three sections, each of which has an increasing slope.

The first section is from -6 to -1, the second section is from 2 to 3, and the third section is from 4 to 6.

This means that the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6.

To confirm this, we can calculate the slope of the graph in each interval. The slope of the graph between two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1).

For the first interval, the slope is (3-(-5))/(-1-(-6)) = 8/-5 = -1.6. This is a negative value, which means the graph is decreasing over this interval. For the second interval, the slope is (4-3)/(3-2) = 1/1 = 1. This is a positive value, so the graph is increasing over this interval.

For the third interval, the slope is (6-4)/(4-2) = 2/2 = 1. This is also a positive value, so the graph is increasing over this interval as well.

Therefore, the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6, which is option D.

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The given statement " the null hypothesis predicts there is a relationship between the variable and a significant difference between the groups." is False because the null hypothesis predicts that there is no relationship between the variables and no significant difference between the groups.

A null hypothesis is a statement that suggests that no relationship exists between two variables. It serves as the baseline assumption and a starting point for researchers to test their alternative hypothesis.

Null hypothesis testing is a statistical method used to compare two mutually exclusive propositions: the null hypothesis and the alternative hypothesis.

In hypothesis testing, the null hypothesis states that there is no significant difference between two groups, while the alternative hypothesis suggests that there is a significant difference between the two groups.

If the observed data deviates significantly from what we would expect under the null hypothesis, we reject it in favor of the alternative hypothesis.

If the observed data does not significantly deviate from what we would expect under the null hypothesis, we fail to reject it.

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After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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The approximate diameter of the largest pillow Sarita can use is 12 inches.

Sarita has 38 inches of fringe to sew around a circular pillow.

To calculate the approximate diameter of the largest pillow she can use, we can use the formula 2 × (fringe length ÷ 3.14) = diameter. In this case, the diameter would be approximately 12 inches (38 ÷ 3.14 = 12.1).

To solve this problem, we need to divide the length of the fringe (38 inches) by the value of pi (3.14). Dividing 38 by 3.14 gives us 12.1. Since we are looking for the approximate diameter, we can round this number down to 12 inches.

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Answer:

B.25

Step-by-step explanation:

use PEMDAS   (Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).)

Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

What is a free operant preference assessment? Free operant preference assessment refers to a behavior analysis process used to determine the preferred stimulus of an individual in a naturalistic environment. This method measures the potential and meaningful reinforcers through the observation of a child's free time. A reinforcement is a consequence that strengthens a behavior.The free operant preference assessment is frequently utilized in the autism field to identify reinforcing stimuli. It is a process of assessing a child's preferred items and actions in a naturalistic setting.The free operant preference assessment is conducted in three different stages: Stage 1: involves observation of preferred items and items that are likely to become potential reinforcers, Stage 2: involves assessing for a hierarchy of items and stage 3 involves using the data gathered to plan the student’s schedule, including reinforcement and non-contingent time periods.

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FREE OPERANT PREFERENCE ASSESSMENT. Providing free access to a variety of stimuli for the purposes of identifying potential reinforcers is best described by Free Operant Preference Assessment.

A free operant preference assessment is a measure of the attractiveness or preference for various stimuli by measuring an individual's time spent with them.

Free access to different stimuli is given to the individual to determine their preferences, which are subsequently used to reinforce the desired behavior or work on behavior modification through behavior analysis.

The steps to conducting a Free Operant Preference Assessment: Prepare the list of stimuli: Initially, you have to prepare a list of stimuli that you believe may act as a reinforcer for the individual, which may include toys, foods, or other things that the person likes.

Prepare the environment: Arrange the stimuli in a room, and let the individual enter it.

Make sure that there is sufficient space to move around and that the person has free access to all of the stimuli.  

Record the time the individual spends with each stimulus. You can observe the person, either directly or through video recording.

 Based on the data obtained, the most preferred and least preferred stimuli can be identified. Then, these preferred stimuli can be used as potential reinforcers.

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The standard deviation of the number of defective bulbs in a sample of 11 light bulbs, where 60% are defective, is 1.53, rounded to two decimal places.

The number of defective bulbs in a sample of 11 light bulbs follows a binomial distribution with parameters n = 11 and p = 0.6, where n is the sample size and p is the probability of a defective bulb.

The standard deviation of the binomial distribution is given by the formula:

σ = sqrt(np(1-p))

where σ is the standard deviation, n is the sample size, p is the probability of success (defective bulb), and (1-p) is the probability of failure (non-defective bulb).

Substituting the values into the formula, we get:

σ = sqrt(11 * 0.6 * 0.4) = 1.53

Therefore, the standard deviation of the number of defective bulbs in the sample is 1.53, rounded to two decimal places.

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The circumference of a gazebo is 47.1 ft

To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).

Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft

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Answer:

y = -3x + 3

Step-by-step explanation:

Knowing that;

Slope Intercept form : y = mx + b

To Find the Slope:

Used any given ordered pair given and use- m =  [tex]\frac{y_2-y_1}{x_2- x_1}[/tex]

Given Table:

X                  Y

1                   0

2                  -3

3                  -6

4                  -9

Solve:

I will use the ordered pair:

(1,0)

(2, -3)

1 and 2 are "x"

0 and -3 are "y"

m [tex]=\frac{-3-0}{2- 1}[/tex]

m [tex]=\frac{-3}{1}[/tex]

m [tex]=[/tex] -3

Now putting the value of m in equation

y = -3x + b

To find the y intercept (b) in the slope intercept formula:

Choose any ordered pair and substitute it in the slope intercept.

Let's choose the first point, (1,0) for calculating y-intercept.

Now plug it in the slope intercept formula:

y = mx + b

y = -3x + 3

Hence, the slope intercept form for that table is:

y = -3x + 3.

RevyBreeze

Answer:

A = 196 units²

Step-by-step explanation:

the area (A) of a regular polygon is

A = [tex]\frac{1}{2}[/tex] perimeter × apothem

here perimeter = 56 and apothem = 7 , then

A = [tex]\frac{1}{2}[/tex] × 56 × 7 = 28 × 7 = 196 units²

that the sum of the angles in a triangle is 180 degrees: C = 180 - A - B

C = 180 - 15 - 120

C = 45 degrees.

A triangle is a geometrical shape that consists of three straight sides and three angles. It is a three-sided polygon, which means that it is a closed figure with three-line segments as its sides. The sum of the interior angles of a triangle is always equal to 180 degrees, which is a fundamental property of triangles. Triangles can have different shapes and sizes, and they can be classified based on their side lengths and angle measures. Some common types of triangles include equilateral triangles (where all three sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where all three sides are different lengths). Triangles are commonly used in mathematics, geometry, and various fields of science and engineering.

by the question.

To solve the triangle, we can use the Law of Cosines, which states that:

[tex]c^{2} = a^{2} + b^{2} -2abcos(c)[/tex]

where c is the length of the third side and C is the angle opposite to it.

Given that one side is 17 and the first angle is 15 degrees, we can use the Law of Sines to find the ratio of the remaining sides:

[tex]a/sin(A) = b/sin(B) = c/sin(C)[/tex]

where A and B are the known angles and a and b are the known sides.

Using this formula, we have:

[tex]a/sin(15) = b/sin(120)[/tex]

or

[tex]b=a/sin(15) = b/sin(120)[/tex]

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The probability of the spinner landing on the letter C is 1/4

To understand the probability of the spinner landing on the letter C, we need to start by looking at the total number of possible outcomes. In this case, there are four possible outcomes, corresponding to the four letters A, B, C, and D.

Since each of the four quadrants on the spinner is equal in size, each of the four letters has an equal chance of being landed on. Therefore, the probability of the spinner landing on the letter C is the number of ways that the spinner can land on C, divided by the total number of possible outcomes.

Since there is only one way for the spinner to land on C, and there are four possible outcomes in total, the probability of the spinner landing on the letter C is 1/4

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The given question is incomplete, the complete question is:

A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner landing on the letter C

Thus, the function for the total amount paid by the manager is: t = 7 +28s.

a mathematical phrase, rule, or legislation that establishes the link between an independent variable and a dependant variable (the dependent variable).

Given data:

Let the number of bags ordered be 's'.

The total amount paid 't'.

Thus, the function for the total amount paid by the manager is:

t = 7 + 28s.

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Answer:

Changes in light and dark.

Step-by-step explanation:

I also do K12 loll

Changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

A sum total of all the living and non-living elements and their effects that influence human life.

Flatworm's eyespots detect changes in light or dark in the environment. They are not capable of detecting distinct shapes or a wide variety of colors.

The eyespots are simple sensory structures that are used to detect the presence or absence of light and dark, and to detect changes in light intensity.

They are primarily used to help the flatworm locate and respond to light, which can be important for activities such as finding food or avoiding predators.

Hence, changes in light or dark is the environmental stimulus which is detected by flatworm's eyespots.

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Answer:

26

Step-by-step explanation:

Robin can go to the movies a maximum of 5 times this month.

Let's start by defining a variable to represent the number of times Robin goes to the movies. Let's call this variable "x".

We know that each movie ticket costs $5, and Robin wants to have at least $12.50 left at the end of the month. This means that the total amount of money she can spend on movies is:

40 - 12.50 = $27.50

We can set up an inequality to represent this:

5x ≤ 27.50

To solve for x, we can divide both sides of the inequality by 5:

x ≤ 5.5

Since we can't go to the movies a fractional number of times, we round down to the nearest whole number.

Therefore, Robin can go to the movies a maximum of 5 times this month.

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The machine part's maximum possible size is 13.5 + 0.07, or 13.57 millimeters.

Two mathematical expressions are shown to be equal in an equation, which is a declaration that is frequently denoted by the equals symbol (=). It implies that the amounts or values represented by both formulations are the same. Equations are a useful tool for representing the relationships between variables and for problem-solving because they allow you to identify the values of the unknown variables that the equation requires. They are frequently applied in the domains of math, physics, engineering, and other sciences as well as in daily activities like budgeting, time management, and cooking.

given

The following absolute value equation could be used to calculate the machine part's height's maximum and minimum values:

0.07 for |height - 13.5|

The machine part's minimum possible size is 13.5 minus 0.07, or 13.43 millimeters.

The machine part's maximum possible size is 13.5 + 0.07, or 13.57 millimeters.

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g(t) = -100 * [tex](1.05)^t[/tex] +[tex](1.05)^(-5)[/tex] 50 is equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated to the right 5 units and up 50 units.

Starting with the function f(t) = -100[tex](1.05)^t[/tex], to translate it 5 units to the right and 50 units up, we can replace t with (t - 5) to shift it to the right, and add 50 to the whole function to shift it up. This gives us:

g(t) = f(t - 5) + 50

g(t) = -100[tex](1.05)^(t - 5)[/tex]+ 50

Simplifying this equation, we can use the properties of exponents to rewrite [tex](1.05)^(t - 5)[/tex] as [tex](1.05)^t[/tex] * [tex](1.05)^(-5)[/tex]:

g(t) = -100[tex](1.05)^t[/tex] *[tex](1.05)^(-5)[/tex]+ 50

g(t) = -100[tex](1.05)^(-5)[/tex] * [tex](1.05)^t[/tex] + 50

So the equation for the function g whose graph is the graph f(t) = -100[tex](1.05)^t[/tex] translated 5 units to the right and 50 units up is:

g(t) = -100[tex](1.05)^(-5)[/tex]* [tex](1.05)^t[/tex]+ 50

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To balance the equation, the right side of the equation must also change by 4%.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=)

To balance the exchange equation, the percentage change on the left side of the equation [tex](\% \triangle M + \% \triangle V)[/tex] must equal the percentage change on the right side of the equation [tex](\% \triangle P + \% \triangle Q)[/tex].

Given that there has been a 3% change in the money supply [tex](\% \triangle M)[/tex] and a 1% change in velocity [tex](\% \triangle V)[/tex], the left side of the equation can be written as:

[tex]\%\triangle M + \%\triangle V = 3\% + 1\% = 4\%[/tex]

To balance the equation, the right side of the equation must also change by 4%. Therefore, the correct answer is:

B. 4%

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Answer:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

To find the expected number of times a two is rolled in 250 rolls:

Expected value = (probability of an event occurring) x (number of trials)

Expected number of twos = 0.1 x 250 = 25

To find the expected number of times a number other than two is rolled in 250 rolls:

Expected number of non-twos = 0.9 x 250 = 225

Therefore, we would expect to roll a two 25 times and a number other than two 225 times in 250 rolls of this biased dice.

Answer:

0.790, or 79%.

Step-by-step explanation:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

We can use the binomial distribution to calculate the probability of getting a certain number of twos in 250 rolls of the dice. The formula for the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k twos

n is the number of trials (250 rolls)

k is the number of successes (getting a two)

p is the probability of success (0.1)

(1-p) is the probability of failure (0.9)

C(n, k) is the number of ways to choose k successes from n trials (n choose k)

To calculate the probability of getting exactly k twos in 250 rolls, we plug in the values for n, k, p, and (1-p) into the formula:

P(X = k) = C(250, k) * 0.1^k * 0.9^(250-k)

We can use a calculator or a software program to find the probabilities for different values of k. Here are some examples:

The probability of getting no twos (k = 0) is P(X = 0) = C(250, 0) * 0.1^0 * 0.9^250 = 0.057

The probability of getting exactly one two (k = 1) is P(X = 1) = C(250, 1) * 0.1^1 * 0.9^249 = 0.153

The probability of getting at least two twos (k >= 2) is the complement of the probability of getting zero or one two:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.057 - 0.153

= 0.790

Therefore, the probability of getting at least two twos in 250 rolls of the biased dice is approximately 0.790, or 79%.

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The equation of the circle with center at (8, 2) that passes through (17, 14) in standard form is (x - 8)² + (y - 2)² = 225

In your problem, we are given that the center of the circle is located at (8, 2) and that the circle passes through the point (17, 14). To find the equation of this circle, we need to use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius of the circle.

To find the radius of the circle, we can use the distance formula between the center of the circle and the point on the circle that is given to us. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) is the center of the circle and (x₂, y₂) is the point on the circle that is given to us.

Plugging in the values we have, we get:

d = √((17 - 8)² + (14 - 2)²) = √(81 + 144) = √(225) = 15

So the radius of the circle is 15.

Now we can plug in the values we have into the standard form of the equation of a circle:

(x - 8)² + (y - 2)² = 15²

which simplifies to:

(x - 8)² + (y - 2)² = 225

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1.  Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ,  V(x) = 1275(1-0.165)ˣ

An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.

In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.

The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.

1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.

2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.

3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.

Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.

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Answer:

Step-by-step explanation: