Question

A technology company uses the function ()=− r of , open x close , equals negative , x cubed , plus 12 , x squared , plus 6 x plus 80 to model expected annual revenue, in thousands of dollars, for a new product, where x is the number of years after the product is released. use the remainder theorem to estimate the revenue in year 5.

Answer 1

To estimate the revenue using the Remainder Theorem, substitute x with 5 in the revenue function R(x) = -x^3 + 12x^2 + 6x + 80. Calculate R(5) to get $285,000 as the estimated revenue in year 5.

Step-by-step explanation:

The question involves using the Remainder Theorem to estimate the expected annual revenue for a technology company. The revenue function given is R(x) = -x^3 + 12x^2 + 6x + 80, where x is the number of years after the product is released. To find the revenue in year 5, we substitute x with 5.

R(5) = -(5)^3 + 12(5)^2 + 6(5) + 80

Proceed with the calculation:

R(5) = -(125) + 12(25) + 30 + 80

R(5) = -125 + 300 + 30 + 80

R(5) = 285 thousand dollars.

Hence, the estimated revenue in year 5 from the Remainder Theorem is $285,000.