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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.6, Problem 62E

(a)

To determine

The function *f* that models the radius as a function of time.

Expert Solution

The value of the function *f* is

**Given:**

The radius of the balloon is increasing at the rate of

The function *f* models the radius as a function of time.

**Calculation:**

Since the function *f* is the function that models the radius as a function of time and the radius of the spherical balloon is increasing at the rate of
*f* is a function of multiplication of increasing rate and time *t*.

The function *f* is written as,

Thus, the value of the function *f* is

(b)

To determine

The function *g* that models the volume as a function of the radius.

Expert Solution

The value of the function *g* is

**Given:**

The function *g* is the function that models the volume as a function of the radius.

**Calculation:**

The volume of sphere with radius *r* is given below,

Since the *g* is the function that models the volume of sphere as a function of the radius, therefore the function *g* is equal to the volume of sphere whose radius is *r*.

The function *g* is written as,

Thus, the value of the function *g* is

(c)

To determine

The value of

Expert Solution

The value of

**Given:**

From part (a), the value of function *f* is given below,

From part (b), the value of function *g* is given below,

**Calculation:**

The composite function

From equation (1), substitute *t* for

Substitute *t* for *r* in equation (2), to find the value of

Substitute

The function

Thus, the value of