# Question in population dynamics using exponential growth rate equation Given population doubles

Question in population dynamics using exponential growth rate equation
Given population doubles in 20 minutes, what is intrinsic growth rate r?
Attempt: Given population doubles, using exponential growth rate we have $\frac{dN}{dt}=2N$ so $N\left(t\right)={N}_{0}{e}^{2t}$ therefore $r=2$, but I have a feeling this is wrong since 20 minutes should be used somewhere around here.
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Alice Harmon
First part.
Since the population doubles in 20 minutes, assuming your t variable is in minutes, you should have that:
$N\left(20\right)=2N\left(0\right)$
Second part.
If you have an exponential growth rate by assumption, $\frac{dN}{dt}=\lambda N$, which results in $N={N}_{0}{e}^{\lambda t}$.
If you evaluate this at times , you'll find that . You can then plug in these expressions into the initial equation comparing the population at these two times to solve for $\lambda$, which should not be equal to 2.