An accountant finds that the gross income, in thousands of dollars, of a small business can be modeled by the polynomial - 0.3t 2 + 8t + 198, where t is the number of years after 2010. The yearly expenses of the business, in thousands of dollars, can be modeled by the polynomial - 0.2t 2 + 2t + 131.

a. Find a polynomial that predicts the net profit of the business after t years.

b. Assuming that the models continue to hold, how much net profit can the business expect to make in the year 2016?

I know that the equation is - 0.1t^2+6t+67, but i don't know how to find part b.

Question

Courtney Mcknight

Mathematics

4 December, 07:13

An accountant finds that the gross income, in thousands of dollars, of a small business can be modeled by the polynomial - 0.3t 2 + 8t + 198, where t is the number of years after 2010. The yearly expenses of the business, in thousands of dollars, can be modeled by the polynomial - 0.2t 2 + 2t + 131.

a. Find a polynomial that predicts the net profit of the business after t years.

b. Assuming that the models continue to hold, how much net profit can the business expect to make in the year 2016?

I know that the equation is - 0.1t^2+6t+67, but i don't know how to find part b.

+3

Answers (1)

Know the Answer?

Loki · Answer 1

A. A polynomial that predicts the net profit after t years:

Income - Expenses =

= ( - 0.3 t² + 8 t + 198) - ( - 0.2 t² + 2 t + 131) =

= - 0.3 t² + 8 t + 198 + 0.2 t² - 2 t - 131 =

= - 0.1 t² + 6 t + 67

b. Important : t is the number of the years after 2010.

So t = 2016 - 2010 = 6.

f (6) = - 0.1 · 6² + 6 · 6 + 67 =

= - 0.1 · 36 + 36 + 67 =

= - 3.6 + 36 + 67 = 99.4 (in thousands of dollars) = $99,400.