If a population growing exponentially doubles | vedclass

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(A) population grows exponentially if sufficient amounts of food resources are available to the individuals. Its exponential growth can be calculated

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$0.2311$

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(A) population grows exponentially if sufficient amounts of food resources are available to the individuals. Its exponential growth can be calculated by the following integral form of the exponential growth equation:$N_{t} = N_{0} e^{rt}$Where,$N_{t} =$ Population density after time $t$$N_{0} =$ Population density at time zero$r =$ Intrinsic rate of natural increase$e =$ Base of natural logarithms $(2.71828)$Given that the population doubles in $3$ years:$N_{t} = 2N_{0}$$t = 3$ yearsSubstituting these values into the equation:$2N_{0} = N_{0} e^{3r}$$2 = e^{3r}$Taking the natural logarithm $(\ln)$ on both sides:$\ln(2) = 3r$$r = \frac{\ln(2)}{3}$Using the value $\ln(2) \approx 0.693$:$r = \frac{0.693}{3} = 0.231$Thus,the intrinsic rate of increase $(r)$ is approximately $0.231$.

If a population growing exponentially doubles in size in $3$ years,what is the intrinsic rate of increase $(r)$ of the population?

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