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

Answer:

2022

9 million

Step-by-step 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