A given bacteria culture initially contains 1500 bacteria and doubles every half hour. The number of bacteria $p$ at a given time $t$ is given by the formula $\displaystyle p(t)=1500 e^{kt}$ for some constant $\displaystyle k$. (You will need to find $\displaystyle k$ to answer the following.)

(a) Find the size of the bacterial population after 80 minutes.

(b) Find the size of the bacterial population after 5 hours.

Remark: Pay attention to the unit of time you choose to use!