Question

C. Using India’s rate of natural increase shown in the table, describe how to calculate the doubling time of India’s population

Answer 1

Answer:

$t \approx 49.860\,years$

Explanation:

The increase rate of population is described by the following ordinary differential equation is:

$\frac{dP}{dt} = \frac{P}{\tau}$

Where $\tau$ is the time constant. The solution of the differential equation is:

$P(t) = P_{o}\cdot e^{\frac{t}{\tau} }$

The time constant in years is found by substituting known variables:

$\ln 1.014 = \frac{1}{\tau}$

$\tau = \frac{1}{\ln 1.014}$

$\tau \approx 71.927\,years$

The doubling time is:

$\ln 2 = \frac{t}{71.927\,years}$

$t = (71.927\,years)\cdot \ln 2$

$t \approx 49.860\,years$