Title: Chain Rule Task
Course: Calculus I

Q: A rock is thrown into a lake, creating a circular ripple that travels outward. As the ripple travels, it displaces sediment on the bottom of the pond.

R(t) is the radius of the ripple at t seconds.

S(r) is the volume of displaced sediment for a ripple of radius r feet.

The total displacement is given by D(t) = S(R(t)).

Determine the average rate of change of D(t) with respect to t between t = 1 and t = 3 using the data below.

t | R(t)
1 | 2
2 | 4
3 | 6
4 | 8
5 | 10
6 | 12
7 | 14
8 | 16
9 | 45
10 | 20

r | S(r)
1 | 5
2 | 10
3 | 15
4 | 20
5 | 25
6 | 30
7 | 35
8 | 40
9 | 45
10 | 50
- 1.5 (Incorrect)
- 3 (Incorrect)
- 5 (Incorrect)
- 6 (Incorrect)
- 10 (Correct)
- 20 (Incorrect)
A: 10