I have this question,
Determine the initial population of a bacterial culture whose growth is exponential if, after $7$ days, the population is $10$ million, and the number triples every in three days.
I know I am supposed to use the formula $P(t)=P(0)e^{kt}$ but I really have no idea how to determine the growth rate. Originally i just tried $k=3$ and $t=7/3$ which just gives $e^{7}$ so i get $$10^{6}=P(0)e^{7}$$
I just have never really had practice with exponentials so i dont know where to go from here, can i just say that $P(0)= \frac{10^{6}}{e^{7}}$?
Consider using $P(t)=P_0\cdot 3^{t/3}$ where $t$ is in days. Then use $P(7)=10,000,000=10^7$ to find $P_0$.