194k views
7 votes
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?

User Khex
by
8.5k points

1 Answer

1 vote

Answer:

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

User Mark Seaborn
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories