# The volume of a growing spherical cell is V = \frac{4}{3} \pi r^3 , where the radius is...

## Question:

The volume of a growing spherical cell is {eq}V = \frac{4}{3} \pi r^3 {/eq}, where the radius is measured in micrometers. Find the average rate of change of {eq}V {/eq} with respect to {eq}r {/eq} when {eq}r {/eq} changes from

(i) 3 to 6 micrometers

(ii) 3 to 4 micrometers

(iii) 3 to 3.1 micrometers

## Average Rate of Change:

Suppose, we have a function {eq}y = f(x) {/eq} and we want to find the average rate of change of this function from {eq}x = a {/eq} to {eq}x = b {/eq}

Then, the average rate of change is:

{eq}f_{avg} = \frac{f(b) - f(a)}{b-a} {/eq}

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The volume function of a growing spherical cell is given by:

{eq}V(r) = \frac{4}{3} \pi r^3 {/eq}

Where {eq}r {/eq} is the radius of the spherical...

Average Rate of Change: Definition, Formula & Examples

from

Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.