Question

the number of employees for a certain company has been decreasing each year by 6%. if the company currently has 670 employees and this rate continues, find the number of employees in 13 years. the number of employees in 13 years will be approximately \\(\square\\). (round to the nearest whole number as needed.)

Explanation:

Step1: Define decay formula

The exponential decay formula is $N(t) = N_0(1 - r)^t$, where $N_0$ is initial number, $r$ is decay rate, $t$ is time.

Step2: Plug in given values

$N_0=670$, $r=0.06$, $t=13$. So $N(13)=670(1 - 0.06)^{13}$

Step3: Calculate the decay factor

First compute $0.94^{13} \approx 0.4420$

Step4: Compute final employee count

$N(13)=670 \times 0.4420 \approx 296.14$

Step5: Round to nearest whole number

Round 296.14 to 296.

Answer:

296