Question

The number N of employees at a company can be approximated by the equation N (x) = 24,787(1.002)x​, where x is the number of years since 1990.

A) Approximately how many employees were there in 2003?
B) Find N′ (13).

Answer 1

(a)25439 Employees

(b)51 employees per year

Explanation:

Given that the number N of employees at a company can be approximated by the equation:

`N (x) = 24,787(1.002)^x`, (where x is the number of years since 1990).

Part A

We want to determine how many employees were there in 2003.

When x=13

`N (13) = 24,787(1.002)^(13)\\\approx 25439$ employees`

Part B

If
`N (x) = 24,787(1.002)^x`

`N'(x)=24787(1.002)^x\ln 1.002\\$Therefore:\\N'(13)=24787(1.002)^(13) * \ln 1.002\\N'(13)=50.83`

In 2003, the number of employees was changing at a rate of approximately 51 employees per year.