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Flauer [41]
3 years ago
7

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

Mathematics
1 answer:
aksik [14]3 years ago
8 0

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

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