Question

Explain how to write a composite function to find the area of the region at time t.

Answer 1

Answer:

$A(t) = \pi (0.5 + 2t)^2$

Step-by-step explanation:

Given

$r(t) = 0.5 + 2t$

$A(r) = \pi r^2$

Required

Determine composite function to find A in terms of t

The interpretation of this question is to determine A(t) and this is solved as follows:

Because:

$r(t) = 0.5 + 2t$

And we want to eliminate r in $A(r) = \pi r^2$

We have to substitute 0.5 + 2t for r in $A(r) = \pi r^2$

$A(r) = \pi r^2$  becomes

$A(t) = \pi (0.5 + 2t)^2$

The solution can be solved further, but it is best left in this form:

$A(t) = \pi (0.5 + 2t)^2$