Question

At a certain company, the monthly salary of project managers can be modeled by the function f(x)= x^4 -10x^2+10,000 where x is the number of years of employment. After how many years would a project manager be eligible for a $20,000 monthly salary?

Answer 1

Answer:

Given

Step-by-step explanation:

Given the monthly salary of project managers modeled by the function

f(x)= x^4 -10x^2+10,000

To know the number of years that a project manager be eligible for a $20,000 monthly salary, we will substitute f(x) = 20,000 and solve for x as shown:

20,000 = x^4 -10x^2+10,000

x^4 -10x^2 = 20000-10000

x^4 -10x^2 = 10,000

x^4 -10x^2 - 10,000 = 0

(x^2)^2-10x^2 - 10000 = 0

let P = x^2

P^2 - 10P -10000 = 0

P = 10±√10²-4(-10000)/2

P = 10 ±√100+(40000)/2

P = 10 ±√40100/2

P = 10 ±200.2/2

P = 210.2/2

P = 105.1

Since P = x^2

105.1 = x^2

x = √105.1

x = 10.25

Hence it will take like after 10 years for the manager to earn a $20,000 monthly salary