Question

From 1985 through 1995, the yearly gross farrm revenue (in millions) in the United States can be modeled by the function R(t)=-t^2+7t+159 and the yearly farm cost (in millions) in the United States can be modeled by the function c(t)=t^2+131 where t is the number of years since 1985. Write a new function, P(t), that models the yearly profit after 1985

Answer 1

The profit function is simply the difference between the revenue function and the cost function. The profit function that models the yearly profit after 1985 is $P(t) = 7t + 28$

Given that:

$R(t) = t^2 + 7t + 159$

$c(t) = t^2 + 131$

The profit function P(t) is calculated as follows:

$P(t) = R(t) - c(t)$

So, we have:

$P(t) = t^2 + 7t + 159 - (t^2 + 131)$

Open brackets

$P(t) = t^2 + 7t + 159 - t^2 - 131$

Collect like terms

$P(t) = t^2- t^2 + 7t + 159 - 131$

$P(t) = 7t + 28$

Hence, the profit function that models the yearly profit after 1985 is $P(t) = 7t + 28$

Read more about profit functions at:

https://brainly.com/question/11334756