 # Question in population dynamics using exponential growth rate equation Given population doubles hapantad2j 2022-05-02 Answered
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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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.