Raindrops falling on the surface of a lake create circular ripples. The radius of the ripple (in inches) increases as a function of time (minutes) according to r(t) = 25t + 2.

Question

1. What is the area of the ripples 2 minutes after the raindrops hit the lake surface?

2. Solve A(r(t)) = 5000 and interpret its meaning.

Answer 1

Part 1.

r(2)=52

and A=π(52)²

Part 2

A(r(t)) means π*r(t)*r(t)=π(25t+2)²

You are asked to solve π(25t+2)²=5000.

What does the solution of this equation mean?