If a population growing exponentially doubles | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

The equation for population size change with a prolonged exponential phase can be converted into a logistic growth equation by multiplying it with:

Identify the phases of the Verhulst-Pearl logistic growth curve in sequence.

The equation of Verhulst-Pearl logistic growth is $\frac{dN}{dt}=rN\left[\frac{K-N}{K}\right]$. From this equation,$K$ indicates:

State the popular humorous anecdote about the dramatic demonstration of how a large population can build up exponentially.

Exponential growth curve is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module