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I really need help plsss!!!

I really need help plsss!!!-example-1
I really need help plsss!!!-example-1
I really need help plsss!!!-example-2
User Headbanger
by
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1 Answer

17 votes
17 votes

Answer:

(a)


image

(b) Rate = 5

(c) Rate = 5

Explanation:

Given

The attached graph

Solving (a): The piece-wise function

For the first line

Calculate the slope of the first line


image

Where


image


image

So, the slope is:


image


image


image

The equation is then calculated as:


image

Where:
image and
image


image


image


image

So, the function of the first line is:


image

For the second line

Calculate the slope of the second line


image

Where


image


image

So, the slope is:


image


image


image

The equation is then calculated as:


image

Where:
image and
image


image


image


image

So, the function of the second line is:


image

Hence, the piece-wise function is:


image

Solving (b): The rate at which customers that buy up to 5lb buy.


image

This question implies that, we determine the rate at which this customer buys.

For
image


image

The slope of the above function is 5.

So, this customer buys at the rate of $5 per lb

Solving (b): The rate at which customers that buy more than 5lb buy the extra pounds above 5lb.

For
image


image

Assume x = 6


image


image


image

Express as 20 + 5


image

Assume x = 7


image


image


image


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Express 10 as 5 * 2


image

So, we have:


image


image

This can be generalized as:


image

For the above functions;

20 represents the amount they buy the first 5

5 represents the rate at which they buy extra pounds above 5

Hence, they buy the extra pounds at the rate of $5 per pound

User Ashish S
by
3.6k points