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

Vedclass · Accepted Answer

$0.2311$

Vedclass · Answer

(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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