Find $an$ exponential function $of$ the form $P(t)=P_0{n}^{\frac{t}{T}}$ that models the situation, and then find the equivalent exponential model $of$ the form $P(t)=P_0{e}^{rt}.$

Doubling time $of3yr,$ initial population $of400.$

Find $an$ exponential function $of$ the form $P(t)=P_0{n}^{\frac{t}{T}}$ that models the situation.

The exponential function $isP(t)=$

$(Use$ integers $or$ fractions for any numbers $in$ the expression.$)$