Application of Composition

Question

A circular oil spill continues to increase 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)=3.14r², where 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.

Answer 1

To write a function of area as a function of time, just substitute r(t) for r in A = π r² :

A(t) = π (0.5+2t)²

I hope this makes sense to you.

Answer 2

A(r(t)) is the composition

you find the radius first (inner function) and then the area second (outer function)

A(r(t))=

A(0.5+2t)=

3.14(0.5+2t)^2