Title: The Chain Rule Task Question
Course: Calculus Videos Project > Section: The Chain Rule

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) | S(t)
1 | 2 | 5
2 | 4 | 10
3 | 6 | 15
4 | 8 | 20
5 | 10 | 25
6 | 12 | 30
7 | 14 | 35
8 | 16 | 40
9 | 18 | 45
10 | 20 | 50
- 1.5
- 3
- 6
- 10
- 20
A: 10