91Ó°ÊÓ

The surface area \(S\) of a cube with edge length \(x\) is given by \(S(x)=6 x^{2}\) for \(x>0 .\) Suppose the cubes your company manufactures are supposed to have a surface area of exactly 42 square centimeters, but the machines you own are old and cannot always make a cube with the precise surface area desired. Write an inequality using absolute value that says the surface area of a given cube is no more than 3 square centimeters away (high or low) from the target of 42 square centimeters. Solve the inequality and write your answer using interval notation.

Using data from Bureau of Transportation Statistics, the average fuel economy \(F\) in miles per gallon for passenger cars in the US can be modeled by \(F(t)=-0.0076 t^{2}+0.45 t+16\), \(0 \leq t \leq 28\), where \(t\) is the number of years since 1980 . Find and interpret the average rate of change of \(F\) over the interval [0,28].