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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.6, Problem 63E

To determine

**To find:** The function that models the surface area of the balloon as a function of time *t*.

Expert Solution

The function that models the surface area of the balloon as a function of time *t* is

**Given:**

The radius of the balloon is increasing at the rate of

**Calculation:**

Since the radius of the spherical balloon is increasing at the rate of

The surface area of the sphere with radius *r* is ,

Substitute

Thus, the function that models the surface area of the balloon as a function of time *t* is