Find f ∘ g of a stone

Question

A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 90 cm/s.

(a) Find a function g that models the radius as a function of time t, in seconds.

Find f ∘ g

Answer 1

We can use a simple distance = rate x time to model this situation.

The radius is the distance from the center of the circle (where the stone landed) to the circle. This is our g(t). The rate is given as 90 cm/s.

The time is t seconds.

This gives us g(t) = 90t.