Given the function
[tex]P(t)=600e^{0.16t}[/tex]When P(t)=3000
[tex]\begin{gathered} P(t)=3000 \\ 600e^{0.16t}=3000 \end{gathered}[/tex][tex]\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}[/tex]Hence, it will take 10.06yr for the population to reach 3000, option F
