A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r (t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A (r) = πr2, where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.

Question

Shayna Bowers

Mathematics

1 August, 05:27

A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r (t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A (r) = πr2, where r is the radius of the circle at time t. Explain how to write a composite function to find the area of the region at time t.

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Answers (2)

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Luna Baxter · Answer 1

You would just put one function inside the other: A (t) =

π (0.5 + 2t) ^2

Henry Clark · Answer 2

Write the composition A compose r : A (r (t)).

The function r (t) is the inside function, or input in function A (r).

Substitute 0.5 + 2t into the area formula in place of r : a (r (t)) = 3.14 (0.5 + 2t) ^2