Question

Plato Help Please 35points

Stephanie is planning to build a boxed garden in her yard. She has not decided on the exact size of the garden, but Stephanie knows she wants the garden to be a rectangle with the length and width in a specific ratio. She also knows the cost of the materials needed to make the garden. Stephanie uses this information to create the following function to model the total cost, C), in dollars, to build a boxed garden that is x feet wide.

C(x)=2x^2+32

What is the average rate of change in the total cost to build the boxed garden as the width increases from 2 feet to 4 feet?


A.$6 per foot
B.$12 per foot
C.$18 per foot
D.$16 per foot

Answer 1

In the equation x is the feet of width.

If the original width is 2 feet, then X^2 = 2^2 = 4

If the width changes to 4 feet, then x^2 becomes 4^2 = 16

The change is 16 - 4 = 12

The answer should be B. $12 per foot.

Answer 2

Answer:

Option B is correct.

Step-by-step explanation:

Given the function which represent the total cost in dollars to build a boxed garden that is x feet wide.

$C(x)=2x^2+32$

we have to find the average rate of change in the total cost to build the boxed garden as the width increases from 2 feet to 4 feet.

$C(2)=2(2)^2+32=8+32=40$

$C(4)=2(4)^2+32=32+32=64$

$\text{Average rate of change=}\frac{C(4)-C(2)}{4-2}$

$=\frac{64-40}{2}=\frac{24}{2}= 12 per foot$

Hence, option B is correct.