Question

I need help with number 5:It says “ The enrollment of a school has been increasing exponentially at a rate of 1.5% per year. The school’s enrollment now is 1,800. Approximately how long ago was the schools enrollment 1200?”

Answer 1

The given exponential growth formula is:

$N=N_0e^{kt}$

It is given that the school's enrollment was 1200, it implies that N₀=1200.

It is given that the school's enrollment now is 1800, it follows that N=1800.

The rate is given as 1.5%, so it follows that k=1.5%=0.015.

Substitute N₀=1200, N=1800, and k=0.015 into the exponential growth formula:

$\begin{gathered} 1800=1200e^{0.015t} \\ \Rightarrow1200e^{0.015t}=1800 \\ \Rightarrow e^{0.015t}=\frac{1800}{1200} \\ \Rightarrow e^{0.015t}=\frac{3}{2} \\ \Rightarrow0.015t=\ln(\frac{3}{2}) \\ \Rightarrow t=\ln(\frac{3}{2})\div0.015 \\ \Rightarrow t\approx27 \end{gathered}$

Hence, the answer is 27 years.

The answer is option A.