The count in a bateria culture is 200 after 16 minutes and 1200 after 38 minutes. Assuming the bacteria count grows exponentially, we can conclude that the population grows by a factor of every 22 minutes, and the population of bacteria after $t$ minutes is $P =$ .

Hint: You may write the population in the form $P = P_0 \, a^{(t-t_0)/h}$.