100 PTS AND BRAINLIEST WRONG ANSWERS REPORTED
The function p(w)=230(1.1)^W represents the number of specialty items produced at the old factory w
weeks after a change in management. The graph represents the number of specialty items produced at the
new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new
factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory.
Show your work.
Answers
Answer:
40; 0.1 and 0.16
Step-by-step explanation:
a. We know that p(w)=230(1.1)^W represents the number of specialty items produced at the old factory.
This equation is in the form of an exponential growth function:
f(x)=a(1+r)^x
where a is the initial value, r is the growth rate, and x is the number of time intervals.
That means that for p(w)=230(1.1)^W:
230 is the initial value, and 0.1 is the growth rate. (1.1-1)
Therefore, for week 0, there were 230 specialty items produced at the old factory.
We can also plug in 0 for w (0 time intervals) to get the same answer
That would look like:
p(0)=230(1.1)^0
p(0)=230(1)
p(0)=230
On the other hand, for the new factory, if you go find 0 on the x-axis, you'll notice that 190 specialty items were produced in week 0.
230-190=40
This means that our answer for a is that 40 more specialty items were produced at the old factory than the new factory.
_____
b. Our first step for this question would be to find the equation for the graph.
We can immediately recognize that this is an exponential growth function, similar to the other equation.
As a reminder, exponential growth functions are in the form: f(x)=a(1+r)^x
We can put it in terms of production and weeks:
p(w)=a(1+r)^w
We know that the initial value is 190 by the graph.
p(w)=190(1+r)^w
Now we just need to find the growth rate:
We can do this by choosing a value (other than the first point) and plugging it in. Let's use (1, 220) which is in the form (w, p)
Plug it in to the equation:
220=190(1+r)^1
220=190(1+r)
Distribute
220=190+190r
Subtract 190 from both sides
30=190r
Divide 190 from both sides
r=0.1578947368 (round how your teacher asks)
Next, all we have to do is find the growth rate for the old factory:
p(w)=230(1.1)^W
1.1=1+r
Therefore, r=0.1
The growth rate at the old factory is 0.1.
When comparing them, we'll realize that the growth rate at the new factory is about 0.06 higher.
#1
For old factory
p(w)=230(1.1)^wSo
week =0[tex]\\ \rm\dashrightarrow p(0)=230(1.1)^0=230(1)=230[/tex]
For nEW factory
On graph y intercept is 190Difference:-
230-190=4040 items were more produced
#2
For old factory
Turn it to p(1+r)^t form where r is rate of change[tex]\\ \rm\dashrightarrow 230(1+0.1)^t[/tex]
Growth rate is 0.1For new factory
(0,190)(1,220)Find slope:-
[tex]\\ \rm\dashrightarrow m=\dfrac{220-190}{1}=30[/tex]
Find growth rate
m/b(b is y intercept)30/1903/190.16New factory has greater growth rate
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Answer:
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Step-by-step explanation:
Hi there!
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Answer:
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Step-by-step explanation:
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[tex] \mathsf\red{♧ANSWER♧}[/tex]
[tex] \mathsf \blue{5 \frac{2}{5} - 3 \frac{7}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{27}{5} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{2( \frac{27}{5} ) - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{54}{10} - \frac{37}{10} }[/tex]
[tex] \blue \implies \mathsf \green{ \frac{17}{10} = 1 \frac{7}{10} = 1.7}[/tex]
Find the derivative of the image below
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[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]
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pls help me i will mark as brilliant
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The question is not clear.
I am not sure how to do for this question! Pls help
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Answer:
wheres the question
Step-by-step explanation:
??????
Two cars, one traveling north and
one traveling east leave a city.
The car traveling north goes X
miles while the car traveling east
has gone ×+4 miles. If the
distance between the cars at this
moment is 20 miles find the
distance the car traveling east has
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multiply the two plynomials
(x + 3)( + 9)
(x + 2)(x + 9)
(x - 8)(x - 6)
im really looking for ways to solve it rather than the solution because it would make my hw alot easier. thanks!
Answers
Answer:
1. x² + 12x + 27
2. x² + 11x + 18
3. x² + -14x + 48
Step-by-step explanation:
When you multiply polynomials, you use FOIL.
First
Outer
Inner
Last
For example, to solve the first polynomial (x + 3)(x + 9), you would multiply the first term in each parenthesis to each other. In this case, it would be x · x, which would be equal to x². The next step would be to multiply the first term in the first parenthesis to the last term in the second parenthesis, which are the outer terms. You get 9x when you multiply x by 9. Then, you multiply the inner terms of the polynomial, which is the last term of the first parenthesis and the first term of the second parenthesis. You get 3x. The last part of FOIL is to multiply the last term in each parenthesis to each other. You would multiply 9 and 3 and get 27. Your answer would be x² + 9x + 3x + 27. Simplify the equation to get x² + 12x + 27. That is your final answer. Do the same thing to the other equations to find the answer. (MAKE SURE TO CHECK THE SIGN OF THE TERMS YOU ARE MULTIPLYING FIRST. )
I hope this helped and please mark me as brainliest!