#### To determine

**To find:** The rate at which the rate of change of the area within the circle is increasing after 1 s.

#### Answer

The rate at which the rate of change of the area within the circle is increasing after 1 s is, 7200π cm2/s.

#### Explanation

**Given:**

A stone which is dropped into a lake that creates a circular ripple whose speed when it travels outward is 60 cm/s.

**Calculation:**

Area inside the ripple at time *t* is A(t)=π(60t)2.

That is, A(t)=3600πt2.

The rate of change of the ripple at time *t* is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 1 s is, A(1)=7200π cm2/s.

#### To determine

**To find:** The rate at which the rate of change of the area within the circle is increasing after 3 s.

#### Answer

The rate at which the rate of change of the area within the circle is increasing after 3 s is, 21,600π cm2/s.

#### Explanation

From part (a), the rate of change of the ripple at time *t* is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 3 s is, A(3)=21,600π cm2/s.

#### To determine

**To find:** The rate at which the rate of change of the area within the circle is increasing after 5 s. What can be concluded from the parts (a), (b) and (c).

#### Answer

The rate at which the rate of change of the area within the circle is increasing after 5 s is, 36000π cm2/s.

#### Explanation

From part (a), the rate of change of the ripple at time *t* is, A'(t)=7200πt.

Therefore, the rate at which the rate of change of the area within the circle is increasing after 5 s is, 36000π cm2/s.

From the parts (a), (b) and (c), it can be concluded that the rate of change increases as time increases.