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Question

Which of the following equations correctly represents the integral form of the equation dN/dt = rN?

A
Nt=N0 ert
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B
N0=Nt ert
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C
N0=ert/Nt
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D
Nt=N0/ert
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Solution

The correct option is A Nt=N0 ert

A population growing in a habitat with unlimited resources exhibits exponential growth. This exponential growth model results in a ‘J’ - shaped growth curve, when population density (N) is plotted in relation to time ‘t’. Population density is the number of people per unit area (per square kilometre).

In the exponential growth model, the curve representing rate of change of population density is represented as

dN/dt = rN

where,

dN represents the change in the population density

dt represents the change in time ‘t’

r represents the intrinsic rate of natural increase. It is the difference between the birth rate and death rate in a population.

This can be represented in the integral form as follows
Nt =N0 ert

Where, Nt is the Population density after time t

N0is the population density at time zero

r is the intrinsic rate of natural increase

e is the base of natural logarithms


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