Question

8. The average attendance at a local high school this year was 950 students. Each year the attendance decreases at a rate of 0.5% per year. What will the average attendance be in three years? a. 945 b. 941 C. 936 d. 893

Answer 1

Exponential decay is represented by the following expression:

$\begin{gathered} F=Ie^{-rt} \\ F=\text{future or final amount} \\ I=\text{ Initial amount} \\ e=\text{Euler's number }\cong2.7183 \\ r=\text{rate of decline (decimal form)=0.005} \\ t=\text{time= 3 years} \end{gathered}$

Now, with the information given we can substitute and solve for F:

$\begin{gathered} F=950\cdot e^{-0.005(3)} \\ F=935.86 \end{gathered}$

Rounding, the average attendance in three years would be 936 students.