Question

A company is using the first two years of its profits to predict what will happen in the future. The profit, p(x), in millions, can be modeled by

the function p(x) =x^2 + 4x + 5, where x, represents the number of years after 2020



- In what year did the company have the largest profit and what was the amount?

Answer 1

2022

9 million

Explanation:

`p(x) =-x^2 + 4x + 5`

To find the value of x when the maximum profit occurs, differentiate the function:

`\implies p'(x)=-2x+4`

set it to zero and solve for x:

`\implies p'(x)=0`

`\implies -2x+4=0`

`\implies x=2`

Therefore, the year in which the company had its largest profit was

2020 + 2 = 2022

Input found value of x into the function:

`p(2) =-(2)^2 + 4(2) + 5=9`

Therefore, the amount was 9 million