Question

The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e0.16t if they haveenough food and the predator population stays constant. After how many years will the population reach 3000?Round to the nearest hundredth.F) 10.06 yrG) 16,31 yrH) 48.65 yrD 19.86 yr

Answer 1

Given the function

$P(t)=600e^{0.16t}$

When P(t)=3000

$\begin{gathered} P(t)=3000 \\ 600e^{0.16t}=3000 \end{gathered}$$\begin{gathered} \text{divide through by 600} \\ e^{0.16t}=\frac{3000}{600} \\ e^{0.16t}=5 \\ 0.16t=in5 \\ 0.16t=1.6094 \\ t=\frac{1.6094}{0.16} \\ t=10.05899yr \\ t=10.06yr(\text{nearest hundredth)} \end{gathered}$

Hence, it will take 10.06yr for the population to reach 3000, option F