The solution is:
The average speed of bicyclist is 120 miles per hours
The speed of wind is 30 miles per hours .
Here, we have,
Given as :
The distance that bicyclist cover = d = 30 miles
The time taken by bicyclist to cover 30 miles = t = 5 hours
Let the average speed of bicyclist = x miles per hours
Let The speed of wind = y miles per hours
Now, biking into wind
The time taken in return by bicyclist = 5 hours
∵ Speed = Distance × time
i.e x + y = d × t
∴ x + y = 30 miles × 5 hours
Or, x + y = 150 mi/h ...........A
Again
Now, biking against wind
The time taken in return by bicyclist = 3 hours
∵ Speed = Distance × time
i.e x - y = d × t
∴ x - y = 30 miles × 3 hours
Or, x - y = 90 mi/h ......B
Solving equation A and B
(x + y) + (x - y) = 150 mi/h + 90 mi/h
Or, (x + x) + (y - y) = 240 mi/h
Or, 2 x + 0 = 240 mi/h
∴ x = 240/2
i.e. x = 120 mi/h
So, The average speed of bicyclist = x = 120 miles per hours
Now, Put the value of x into eq B
∵ x - y = 90 mi/h
Or, 120 mi/h - y = 90 mi/h
∴ y = 120 mi/h - 90 mi/h
I.e. y = 30 mi/h
So, The speed of wind = y = 30 miles per hours
Hence, The average speed of bicyclist is 120 miles per hours
And The speed of wind is 30 miles per hours .
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complete question:
Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip. What is the bicyclist's average speed in the air? What is the speed of the wind?
Assume the probability of rain on any given independent day is 0.23. What is the average number of days it rains for the first time?
The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.
We have,
A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
The probability that a particular song is played is 0.23,
As can be seen that the problem is of combination, so we have to choose 5 out of 7,
Calculate the combination as shown below,
⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2
⁷C₅ = 7 × 6 / 2
⁷C₅ = 21
Calculate the probability as shown below,
P = ⁷C₅ × (0.23)⁵ × (0.77)²
P = 0.008
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complete question;
During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.
Find x and the measurement of each angle.
Answer:
x = 8, m2 = 78, m4 = 102, m6 = 78, m7 = 78,
Step-by-step explanation:
Please help as soon as possible, thank you in advance
The logo that fits the requirement is the circle logo i.e. logo 1
Calculating the area and the width in metersFrom the question, we have the following parameters that can be used in our computation:
The figures that represent the logos
For the circle logo, we have
Area = 22/7 * 1/2 * 1/2
Convert units to feet using the scale
Area = 22/7 * 1/2 * 7 * 1/2 * 7
Evaluate
Area = 38.5 square feet
Also, we have
Width = 2 * 1/2 * 7 feet
Width = 7 feet
For the plus-shaped logo, we have
Area = 5 * 1/2 * 1/2
Convert units to feet using the scale
Area = 5 * 1/2 * 7 * 1/2 * 7
Evaluate
Area = 61.25 square feet
Also, we have
Width = 3 * 1/2 feet * 7
Width = 10.5 feet
Hence, the logo that fits the requirement is the circle logo i.e. logo 1
This is because its area is not up to the maximum area (40 square feet) and the width is greater than the minimum width (4 feet)
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Give the domain and range. On a coordinate plane, points are at (negative 2, negative 1), (0, 1), (2, 3). a. domain: {2, 0, 2}, range: {1, 1, 3} b. domain: {–1, 1, 3}, range: {–2, 0, 2} c. domain: {–2, 0, 2}, range: {–1, 1, 3} d. domain: {1, 1, 3}, range: {2, 0, 2} Please select the best answer from the choices provided A B C D
Answer:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Step-by-step explanation:
From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.
The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.
In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.
Therefore, the correct answer is:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
given f (x) = 4x^2+6x+9 find (-7)
The value of f(-7) is 172.
To find the value of f(-7) for the given function f(x) = 4x^2 + 6x + 9, we substitute -7 for x in the function and evaluate it.
f(-7) = 4(-7)^2 + 6(-7) + 9
Simplifying the equation:
f(-7) = 4(49) - 42 + 9
= 196 - 42 + 9
= 163 + 9
= 172
Therefore, f(-7) = 172.
By substituting -7 into the function, we obtained the value of 172. This means that when x is equal to -7, the corresponding value of the function f(x) is 172.
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A rectangle floor is 9 yards long and 3 yards wide what is the area of the floor in square feet
Answer:
1. Find the area of the rectangle in square yards. In this case, the area is 9 yards * 3 yards = 27 square yards.
2. Convert square yards to square feet. There are 9 square feet in 1 square yard. So, the area of the rectangle in square feet is 27 square yards * 9 square feet/square yard = 243 square feet.
Therefore, the area of the rectangle floor in square feet is 243 square feet.
Answer:243
Step-by-step explanation:
(9x3) x (3x3)
27 x 9 = 243
Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-10
The graph of the inverse function is given by the image presented at the end of the answer, and the correct option is given by option 3.
How to obtain the inverse function?The parent function for this problem is the cube function translated up two units, hence it is defined as follows:
y = x³ + 2.
To obtain the inverse function, first we must exchange the variables x and y on the definition of the function, as follows:
x = y³ + 2.
Then we must isolate the variable y, as follows:
[tex]y^3 = x + 2[/tex]
[tex]y = \sqrt[3]{x + 2}[/tex]
Which has the correct dashed graph given by option 3 on the image given.
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add or subtract (3x^2-7x-4)-(6x^2-6x+1)
pls help
answers
–3x^2 – x –5
–3x^2 –13x + 5
9x^2 – x + 5
3x^2 – 13x – 5
Answer:
-3x² - x - 5
Step-by-step explanation:
(3x² - 7x - 4) - (6x² - 6x + 1) =
= -3x² - x - 5
Carson and his children went into a restaurant where they sell hamburgers for $6 each and tacos for $2.50 each. Carson has $65 to spend and must buy a minimum of 12 hamburgers and tacos altogether. If Carson decided to buy 8 tacos, determine the maximum number of hamburger that he could buy.
answer the following steps to find the volume of the composite figure. what is the volume the 3 mm tall cone? what is the volume of the cylinder? what is the volume of the 1 mm tall cone? what is the volume of the composite figure?
We are unable to determine the volumes of the individual components and the composite figure due to missing data on the radii and precise component configurations.
We must determine the volumes of the three separate parts—a cylinder, a 1 mm tall cone—in order to get the volume of the composite figure.
The 3 mm tall cone's volume is:
The formula [tex]V = (1/3)r^{2} h,[/tex] where r is the radius of the base and h is the height, determines the volume of a cone.
We must determine the radius because the cone's height is 3 mm. We are unable to determine the volume of the 3 mm tall cone without additional information.
Dimensions of the cylinder:
The formula V = r2h, where r is the radius of the base and h is the height, determines the volume of a cylinder.
We are unable to determine the volume of the cylinder without precise measurements for its height and radius.
Volume of the 1 mm tall cone: Once more, in order to calculate the volume of the 1 mm tall cone, we need to know the radius of the base. Without this additional information, we are unable to do so.
The composite figure's volume:
We would need to know the sizes and configurations of the different parts (cones and cylinder) within the composite figure in order to determine its volume.
We are unable to determine the volume of the composite figure without this information.
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Solve for x.
-3
X=
X
= -48
Answer:x = {-4, 4}
explanation:
Type the correct answer in the box. Use numerals instead of words.
For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
2
3
÷
2
4
+
(
3
4
+
1
6
)
÷
1
3
The expression has a value equal to
Answer:67/24
hope it helps bye
The expression equivalent to the given numerical expression is 67/24.
The given numerical expression is 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3.
Here, 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3
= 2/3 ÷ 16+(9/12 +2/12)÷1/3
= 2/3 × 1/16 +11/12 ×3/1
= 2/48 + 33/12
= 1/24 + 33/12
= 1/24 + 66/24
= 67/24
Therefore, the expression equivalent to the given numerical expression is 67/24.
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The graph shows the cube root parent function.
-5
5
Which statement best describes the function?
A
The statement of the function is (b) when x > 0, the graph is positive
Describing the transformation of the function f(x)From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
In the graph, we can see that
The graph of the function passes through (0, 0)
This means that
When x > 0, the graph is positive
When x < 0, the graph is negative
Hence, the statement of the function is (b)
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when the football game started, there were twice as many eagle fans as spartan fans. At the end of the first quarter, 500 extra eagle fans came on busses. The total attendance at the game was 4790. How many people attended from each school?
Answer:
2860 Eagle fans and 1430 Spartan fans-------------------
Let E represent the number of Eagle fans and S represent the number of Spartan fans at the start of the game.
We can set up two equations using the given information:
1) E = 2S (twice as many Eagle fans as Spartan fans) 2) E + S + 500 = 4790 (total number, including the extra 500 fans)Now we can solve the equations.
From equation (1), we can replace E in equation (2), the solve for S:
(2S) + S + 500 = 4790 3S + 500 = 47903S = 4290 S = 1430Now find the number of Eagle fans using equation (1):
E = 2S E = 2(1430) E = 2860In 2004, a school population was 2122. By 2009 the population had grown to 2647.
1) How much did the population grow between the year 2004 and 2009?
The population grow by 24.7% between the years 2004 and 2009
Calculating how much the population grow between the yearsfrom the question, we have the following parameters that can be used in our computation:
Population in 2004 = 2122
Population in 2009 = 2647
The growth of the population between the years is calculated as
Percentage = Population in 2009/Population in 2004 - 1
Substitute the known values in the above equation, so, we have the following representation
Percentage = 2647/2122 - 1
Evaluate
Percentage = 24.7%
Hence, the population grow between the years by 24.7%
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QUESTIONS 1. Explain and illustrate the difference between and (4) 2. Explain and illustrate the difference between ratio and proportional reasoning. Do not copy definitions from any source but use your own understanding. (4) 3. Illustrate with a drawing or diagram what "fifth" means in each of the following instances: ● ordinal number ● unit fraction 4. Show with a diagram 3, using the following: 1.1 the area model 1.2 set mode 1.3 the length model (3) 2. A rectangular piece of paper has a perimeter of 54 cm. Its length is 1 of its width. Find its dimensions. (3) 3. If the given regular hexagon represents one whole: 3.1 Show three sixths. 3.2 Write the equivalence 6.1 above. 3 Represent+ in the figure given to prove that a set of two halves 6 make a whole. (4) 6.3.1 Draw a number line showing a whole made of six equal parts. Show the sum of two halves on the same number line. (1) (1) (2) (3)
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
How to solve1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.
Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.
Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.
Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.
To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.
1.2 The set model:
To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.
Step 5/5
Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:
Now we know that the perimeter of the rectangle is given by the formula:
So, for this rectangle:
54 = 2(5x + x)
Simplifying and solving for x, we get:
54 = 2(6x)
27 = 6x
x = 4.5 cm
Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
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Help me figure this out
Answer:
35
Step-by-step explanation:
perimeter = sum of the lengths of the sides
In a parallelogram, opposite sides are congruent.
Two sides have length 7.5 cm.
We need the length of the top and bottom sides.
area = base × height
62 cm² = base × 6.2 cm
base = (62 cm²)/(6.2 cm)
base = 10 cm
Two sides have length 10 cm.
perimeter = 7.5 cm + 7.5 cm + 10 cm + 10 cm
perimeter = 35 cm
Find the equation of the line.
Use exact numbers.
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line
m = [tex]\frac{1-7}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
the line crosses the y- axis at (0, 7 ) ⇒ c = 7
y = - 3x + 7 ← equation of line
The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7
Writing the equation of the line in slope-intercept form.The linear graph represents the given parameter
For the graph, we have the points
(0, 7) and (25, 0)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 7
Using the point (2.5, 0) on y = mx + 7, we have
m(2.5) + 7 = 0
2.5m + 7 = 0
Evaluate
m = -2.8
So, we have
y = -2.8x + 7
Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7
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The following figure is made of 2 triangles. Figure Triangle A Triangle B A Whole figure 9 Find the area of each part of the figure and the whole figure. 7 B 3 Area (square units)
Area of triangle A = 13.5 square units
Area of triangle B = 10.5 square units
Total area of figure = 24 square units
In the given figure,
It consist of two triangles
Now for triangle A :
Height = 3
Base = 9
Since we know that,
Area of triangle = (1/2) x base x height
= 0.5 x 9 x 3
= 13.5 square units
Now for triangle B :
Height = 3
Base = 7
Since we know that,
Area of triangle = (1/2) x base x height
= 0.5 x 7 x 3
= 10.5 square units
Now the total are of figure is sum of are of both triangles,
Therefore,
total area of figure,
⇒ 13.5 + 10.5
⇒ 24 square units
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The missing figure of question is attached below:
100 points! A list of rational numbers is given.
one and four fifths, negative seven fourths, forty-one percent, negative 1.3
Part A: Rewrite all the values into an equivalent form as fractions. (3 points)
Part B: Rewrite all the values into an equivalent form as decimal numbers. (3 points)
Part C: List the given rational numbers from greatest to least. (3 points)
Part D: How did you determine their order? Please explain your answer. (3 point)
The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8
Given are the list of the rational numbers, so,
1 4/5, -7/4, 41% and -1.3
So,
1) The fraction form :-
a) 1 4/5 = 9/5
b) -7/4
c) 41% = 41/100
d) -1.3 = 13/10
2) The decimal form :-
a) 1 4/5 = 9/5 = 1.8
b) -7/4 = -1.75
c) 41% = 41/100 = 0.41
d) -1.3 = 13/10 = -1.3
3) The ascending order of the rational numbers =
You can arrange them by seeing the value and sign,
-1.75 < -1.3 < 0.41 < 1.8
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When you order a salad from Nelly's Deli, you can choose from 5 different base salads, 3 different proteins, and 6 different dressings. How many different combinations for a salad are possible?
Answer:
90
Step-by-step explanation:
This type of problem is an example of combinations. In this case, in one salad, it states that you can chose between 5 bases, 3 proteins, and 6 dressings.
In this problem, you would have to multiply all numbers together.
In this case, 5(bases)x3(protiens)x6(dressings)=90
I hope this helps you!
Solve the system using substitution. Show all work.
-12x + 5y = 9
y = 2x - 5
Solution of the given system is,
x = 8
y = 11
The given system of equation
-12x + 5y = 9 ....(i)
y = 2x - 5 ...(ii)
Now we have to solve it by using substitution method.
So put value of y from equation (ii) into equation (i)
Therefore,
⇒ -12x + 5y = 9
⇒ -12x + 5(2x - 5) = 9
⇒ -12x + 10x - 25 = 9
⇒ -2x = 16
⇒ x = 8
Now put the values of x into (ii) we get,
⇒ y = 2x8 - 5
⇒ y = 11
Hence,
solutions be ,
x = 8
y = 11
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find the difference between points (3,5) and (-1,5)
b'
Let the given points be A(3,-5) and B(5,-1).
AB= sqrt of (5−3) ² +(−1+5)²
= sqrt of 4+16
= sqrt of 20
=2 sqrt of 5 units
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment.
(b) Assuming his suspicion that 7.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 14 customers buy a magazine? Give your answer as a decimal number rounded to two digits.
(c) What is the expected number of customers from this sample that will buy a magazine?
The experiment is binomial , probability that 3 out of 14 customers buy a magazine is 0.06 and the expected value is 1.036.
Part AThe experiment described is binomial because it satisfies the following conditions:
There are a fixed number of trials, which is 14 in this case.Each trial has two possible outcomes: The outcome of each trial is whether or not a customer buys a magazine. The probability of success is constant. 7.4%The trials are independent: Each customer's behavior is independent of others.Part BThe probability that exactly 3 out of the first 14 customers buy a magazine. Using the binomial probability formula:
[tex]P(X = k) = (nCk) \times (p^k) \times {q}^{n - k} [/tex]
Where:
n = number of trials (14 in this case)
k = number of successful trials (3 in this case)
p = probability of success (7.4% or 0.074)
q = 1-p
Plugging in the values:
P(X = 3) = (14C3) × (0.074³) × 0.926¹¹
P(X= 3) = 0.0633
Part CThe expected number of customers from this sample that will buy a magazine can be calculated using the formula:
E(X) = n × p
Where:
- n is the number of trials
- p is the probability of success
Plugging in the values:
E(X) = 14 × 0.074 = 1.036
Therefore, the experiment is binomial and the expected value is 1.036.
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The distributions of the periods is that using the five number summary is that
The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher medianB. The box and whisker plot of the periods is attached
A. Comparing the distributions of the periodsFrom the question, we have the following parameters that can be used in our computation:
7th Period
66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96
3rd Period
52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97
The distributions of the periods will be compared using the five-number summaries
Using a graphing tool, the five-number summaries are:
7th Period
Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 963rd Period
Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97B. Creating a box and whisker plot of the periodsThe box and whisker plot of the periods is added as an attachment
From the box and whisker plot attached, we can see the five-number summaries of the periods
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A wolf leaps out of the bushes and takes a hunter by surprise. Its trajectory can be mapped by the equation f(x) = −x2 + 11x − 18. Write f(x) in intercept form and find how far the wolf leaped using the zeros of the function. (1 point)
y = (x − 3)(x + 6); the wolf leaped a distance of 9 feet using zeros −6 and 3
y = −(x − 3)(x − 6); the wolf leaped a distance of 3 feet using zeros 3 and 6
y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9
y = (x + 2)(x − 9); the wolf leaped a distance of 11 feet using zeros −2 and 9
y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9. Therefore, option B is the correct answer.
Given that, trajectory can be mapped by the equation f(x) = -x² + 11x - 18.
Here, -x² + 11x - 18=0
-x² + 9x+2x - 18=0
-x(x-9)+2(x-9)=0
(x-9)(-x+2)=0
x-9=0 and -x+2=0
x=9 and x=2
Therefore, option B is the correct answer.
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Which of the following will have a smaller standard deviation, if nine observations are randomly drawn from a population?
The distribution of the individual observations, X
The distribution of the sample means,
x
¯
This cannot be determined from the information given.
The distribution of the sample means will have a smaller standard deviation
Identifying which will have a smaller standard deviationFrom the question, we have the following parameters that can be used in our computation:
Observations = 9
The population is not given
However by the theorem of the central limit; we understand that
The distribution of the sample means will always have a smaller standard deviation
This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation
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What is the equation of the circle with center at (9,5) that passes through (13,7)? Write your answer in standard form.
The equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.
we have Center at (9, 5) and passes thorough (13, 7).
To find the equation of a circle with center (h, k) and a point (x, y) on the circle, we can use the standard form equation of a circle:
(x-h)² + (y-k)² = r²
So, (x - 9)² + (y - 5)² = r
Since the circle passes through (13, 7), then
(13 - 9)² + (7 - 5)² = r²
²4 + (2)² = r²
16 + 4 = r²
20 = r²
So, the equation of circle is
(x - 9)² + (y - 5)² = 20
Therefore, the equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.
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can my a value be negative in a exponential function
Yes, the coefficient of a value can be negative in an exponential function.
How is this possible?A coefficient in mathematics is a multiplicative factor in some term of a polynomial, series, or expression; it is generally a number, although it can be any expression.
Recall that the general form of an exponential function is f(x) = a^(bx + c), where a is the base.
This can be negative or positive. But cannot be equal to zero. A negative exponential function can model the decay of a radioactive substance or, in accounting, depreciation of an asset.
Thus, it is correct to state that , the coefficient a value can be negative in an exponential function.
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HELP DUE!! HELP ASAP!!
The time needed before the doctor administers the medication again is given as follows:
d) 22.2 hours.
How to model the situation?The exponential function giving the amount of the medicine in the patient's bloodstream after t hours is given as follows:
[tex]A(t) = 500(0.93)^t[/tex]
The medication will be applied when the amount is given as follows:
A(t) = 100.
Hence the time needed is obtained solving the exponential function as follows:
[tex]100 = 500(0.93)^t[/tex]
[tex](0.93)^t = \frac{100}{500}[/tex]
[tex](0.93)^t = 0.2[/tex]
The logarithm of base 10 is the inverse of the exponential, hence:
[tex]t = \frac{\log{0.2}}{\log{0.93}}[/tex]
t = 22.2 hours.
Which is the time needed before the doctor administers the medication again.
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