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

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Using India's Rate Of Natural Increase Shown In The Table, Describe How To Calculate The Doubling Time

Answers

Answer 1

Using an exponential function, it is found that the doubling time of India's population is of 50 years.

Exponential function

An exponential function of initial value A(0) and growth rate r is defined according to the following rule:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which t is the time in years after the initial value A(0) was taken.

From the given table, the growth rate of India's population is as follows:

r = 0.014. (as a decimal).

Hence the function is:

[tex]A(t) = A(0)(1.014)^t[/tex]

The doubling time is the value of t for which:

A(t) = 2A(0).

Hence it can be found solving the exponential function as follows:

[tex]A(t) = A(0)(1.014)^t[/tex]

[tex]2A(0) = A(0)(1.014)^t[/tex]

[tex](1.014)^t = 2[/tex] (simplify A(0))

[tex]\log{(1.014)^t} = \log{2}[/tex] (the time can be moved to the front of the log -> log power rule).

[tex]t\log{1.014} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.014}}[/tex]

t = 50 years -> rounded -> doubling time of India's population.

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