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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.

Respuesta :

HomertheGenius
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.

a. = - 0.1 t² + 6 t + 67

b. = $99,400.

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