Question

The number of employees for a certain company has been decreasing each year by3%. If the company currently has720 employees and this rate continues, find the number of employees in5 years.Part 1The number of employees in5 years will be approximatelyenter your response here.(Round to the nearest whole number as needed.)

Answer 1

Exponential decay formula

`f(x)=a(1-r)^x`

where:

• f(x): exponential decay function

,

• a: initial amount

,

• r: rate of decay, as a decimal

,

• x: time

In this case, f(x) models the number of employees after x years, the initial amount is a = 720 employees, and the rate of decay is r = 0.03 (= 3/100). Substituting these values into the formula, and evaluating for x = 5 years, we get:

`\begin{gathered} f(x)=720(1-0.03^{})^x^{} \\ f(x)=720(0.97)^x \\ f(5)=720(0.97)^5 \\ f(5)\approx618 \end{gathered}`

The number of employees in 5 years will be approximately 618