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

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.

Vocaloid · Answer

Notice what happens if you plug r(t) = 0.5 + 2t into the area equation for r. You’ll eliminate r and get an equation for A in terms of t.