Question

The number of items made per week by a company is given by n(t) = 40t + 2000, where t is time in weeks. The profit of the company in thousands of dollars depends on the number of items provided, according to the formula P(n) = 3 √n-1000

Determine the equation for weekly profit of the company as a function of time.

Use the equation from a) to determine when the weekly profit first reaches $150 000.

Answer 1

assuming you meant
P(n) = 3√(n-1000) or else we would have a negative profit for reasonable
values of n

P(n) = 3√(40t+ 2000 - 1000)
= 3√(40t + 1000)

so when P(n) = 150
3√(40t + 1000) = 150
√(40t + 1000) = 50
square both sides:
40t + 1000 = 2500
40t = 1500
t = 37.5 weeks