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 dNdt=2N so N(t)=N0e2t therefore r=2, but I have a feeling this is wrong since 20 minutes should be used somewhere around here.
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Answers (1)

Alice Harmon
Answered 2022-05-03 Author has 12 answers
First part.
Since the population doubles in 20 minutes, assuming your t variable is in minutes, you should have that:
N(20)=2N(0)
Second part.
If you have an exponential growth rate by assumption, dNdt=λN, which results in N=N0eλt.
If you evaluate this at times t=0 and t=20, you'll find that N(0)=N0 and N(20)=N0e20λ. You can then plug in these expressions into the initial equation comparing the population at these two times to solve for λ, which should not be equal to 2.
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