Question

The overall cost of carpet and installation from a particular company is represented by the function, where x represents the square footage of the carpet.

P(x) = $2.90x + $103.00

What is the average rate of change over the interval [2,000, 2,500]?

A. $2.90 per square foot
B. $4.85 per square foot
C. $0.34 per square foot
D. $1.03 per square foot

Answer 1

The function is linear, so its rate of change is the same everywhere. That rate of change is the coefficient of the variable x, so is $2.90. Since the units of x are feet, and the units of P(x) are dollars, the rate of change $2.90 must be ...

... A. $2.90 per square foot