Question

The question is :

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.

Answer 1

You are correct, the profit is modeled by:
-0.1t² + 6t + 67

We are also told that "t" is the number of years after 2010. So in 2016, the value of t will be 6. We substitute this into the equation we formed:

-0.1(6²) + 6(6) + 67
= 106.6 thousand dollars