A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.
Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work

Question

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.

The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.
 Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work

mathstudent55 · Answer

This is composition of functions.
Start by writing the function A(r).
Then replace r in the function with r(t).