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The formula for exponential population growth is -
A
$\dfrac{dt}{dN} = rN$
B
$\dfrac{dN}{rN} = dt$
C
$\dfrac{rN}{dN} = dt$
D
$\dfrac{dN}{dt} = rN$
Detailed Solution
When resources (food and space) are unlimited, each species can realise fully its innate potential to grow in number; the population then grows in an exponential or geometric fashion.
If $N$ is the population size, $b$ the per capita birth rate and $d$ the per capita death rate, then the change in $N$ during time $t$ is $\dfrac{dN}{dt} = (b - d) \times N$
Let $(b - d) = r$, the intrinsic rate of natural increase.
Then $\dfrac{dN}{dt} = rN$
Its integral form is $N_t = N_0 e^{rt}$, and plotting $N$ against time gives a J-shaped curve.
So the formula for exponential population growth is $\dfrac{dN}{dt} = rN$.
If $N$ is the population size, $b$ the per capita birth rate and $d$ the per capita death rate, then the change in $N$ during time $t$ is $\dfrac{dN}{dt} = (b - d) \times N$
Let $(b - d) = r$, the intrinsic rate of natural increase.
Then $\dfrac{dN}{dt} = rN$
Its integral form is $N_t = N_0 e^{rt}$, and plotting $N$ against time gives a J-shaped curve.
So the formula for exponential population growth is $\dfrac{dN}{dt} = rN$.