Question

A businessman models the number of items (in thousands) that his company sold from 1998 through 2002 as N(x) = −0.2x3 + x2 − 2x + 9 and the average price per item (in dollars) as P(x) = 0.6x + 5, where x represents the number of years since 1998. Enter a polynomial R(x) that can be used to model the total revenue for this company.

Answer 1

Basically, you are asked to find the equation for total revenue. In economics, total revenue is equal to the the quantity multiplied with price.

Total Revenue = Price*Quantity
Thus,
R(x) = P(x) * N(x)
R(x) = (0.6x + 5)(−0.2x³ + x² − 2x + 9)
R(x) = -0.12x⁴ + 0.6x³ - 0.12x² + 5.4x - x³ + 5x² - 10x + 45
R(x) = -0.12x⁴ - 0.4x³ + 4.88x² - 4.6x + 45