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 aft

$$\\P=500e^{kt}\\\\ 800=500e^{k*1}\\\\ 1.6=e^k\\\\ ln(1.6)=k\\\\ so\\\\ P=500e^{ln(1.6)*t}\\\\ when\;\; t=3\\\\ P=500e^{ln(1.6)*3}\\\\ P=500e^{3ln(1.6)}\\\\$$

$${\mathtt{500}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{\left({\mathtt{3}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{1.6}}\right)}\right)} = {\mathtt{2\,047.999\: \!999\: \!999\: \!999\: \!5}}$$

There will  be 2048 insects.   

A population of insects obeys the law of uninhibited growth. If there are 650 insects to begin with, and there are 800 after 2 days, how many will theure be after 5 days?