Question

Which of the following equations correctly represents the exponential population growth curve ?

• A. $dN/dt=rN$
• B. $dN/dt=rN\left(\frac{K-N}{K}\right)$
• C. $N_t=N_0{e}^{rt}$
• D. Both (a) and (c)

Answer 1

Answer: (D)

If any species is flourishing under unlimited resources, it would reach exponential growth which can be depicted by equation :
$\frac{dN}{dt}=N$
Where, $N=$ population density at time $t;r=$ intrinsic rate of natural increase.
If we derive the integral form of the exponential growth equation, it can be written as
$N_t=N_0{e}^{rt}$
Where $N_t=$ population density after time $t$; $N_0=$ population density at time zero; $r=$ intrinsic rate of natural increase; $e$ is the base of natural logarithm.