Question

Select the correct answer.

Tracy wants to make a cylindrical model. The height of the cylindrical model, H(V), in inches, is modeled by this

equation, where Vis the volume of the cylindrical model, in cubic inches.

H(V) = 2. 6937

What is the average rate of change of the model's height when its volume changes from 512 cubic inches to

1,000 cubic inches?

The model's height increases by approximately 21. 52 inches for every 1-cubic-inch increase in its volume.

The model's height increases by approximately 0. 022 inch for every 1-cubic-inch increase in its volume.

The model's height increases by approximately 0. 011 inch for every 1-cubic-inch increase in its volume.

The model's height increases by approximately 26. 9 inches for every 1-cubic-inch increase in its volume.

Answer 1

The average rate of change of the height function is slope of the height function

The model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.

How to determine the average rate of change?

The height function is given as:

$H(V) = 2.69\sqrt[3]{V}$

When V = 512, the function becomes

$H(512) = 2.69\sqrt[3]{512}$

$H(512) = 21.52$

Similarly;

When V = 1000, the function becomes

$H(1000) = 2.69\sqrt[3]{1000}$

$H(1000) = 26.9$

The average rate of change is then calculated as:

$H' = \frac{H(1000) - H(512)}{1000 - 512}$

This gives

$H' = \frac{26.9 - 21.52}{1000 - 512}$

$H' = \frac{5.38}{488}$

Evaluate the quotient

$H' = 0.01102459016$

Approximate

$H' = 0.011$

Hence, the model's height increases by approximately 0.011 inch for every 1-cubic-inch increase in its volume.

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