Suppose That at Any Time T, a Colony of Fruit $\mathrm { P } ( \mathrm { t } ) = a \mathrm { e } ^ { \mathrm { b } t }$

Short Answer

Suppose that at any time t, a colony of fruit flies is growing at a rate equal to one half the current size of the colony. Find a formula which gives the size of the colony at time t if there were originally 500 fruit flies present.
Enter your answer exactly in the form: $\mathrm { P } ( \mathrm { t } ) = a \mathrm { e } ^ { \mathrm { b } t }$