arithmetic and composition problem (help is much appreciated!)

Question

The area of a circular wave expands across a still pond such that its radius increases by 9 cm each second. Write a formula for the area A of the circle as a function of time t since the wave begins: 

A=

Answer 1

Hello, Hailey,

Area of a circle is πr² or A = πr², where r is the radius and A is the area.

The radius, r, changes as a function of time. I'll assume at time 0 the radius is zero (e.g., the rock hasn't hit the water yet). The radius increases 9 cm every second. So we can write:

r = 9(cm/sec)*t, where time is time is seconds, At 1 second the radius is 9 cm, and so on.

Now we can substitute this into the first equation to give:

A = π*(9t)².

I hope this helps,

Bob