The population of a colony of a certain insect obeys the law of uninhibited growth. If there are 500 insects initially and there are 800 after one day, what is the size of the colony after 3 days?
+118608
$$\\P=500e^{kt}\\\\
800=500e^{k*1}\\\\
1.6=e^k\\\\
ln(1.6)=k\\\\
so\\\\
P=500e^{ln(1.6)*t}\\\\
when\;\; t=3\\\\
P=500e^{ln(1.6)*3}\\\\
P=500e^{3ln(1.6)}\\\\$$
$${\mathtt{500}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{3}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{1.6}}\right)}\right)} = {\mathtt{2\,047.999\: \!999\: \!999\: \!999\: \!5}}$$
There will be 2048 insects. 
+118608
$$\\P=500e^{kt}\\\\
800=500e^{k*1}\\\\
1.6=e^k\\\\
ln(1.6)=k\\\\
so\\\\
P=500e^{ln(1.6)*t}\\\\
when\;\; t=3\\\\
P=500e^{ln(1.6)*3}\\\\
P=500e^{3ln(1.6)}\\\\$$
$${\mathtt{500}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{3}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{1.6}}\right)}\right)} = {\mathtt{2\,047.999\: \!999\: \!999\: \!999\: \!5}}$$
There will be 2048 insects.
