Question

Which of the following equation correct represents the exponential population growth curve?

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

Answer 1

The correct option is D Both A and C

• In exponential growth, a population's per capita (per individual) growth rate stays the same regardless of population size, making the population grow faster and faster as it gets larger.
  
• When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve.
• Exponential growth is represented by the equation dN/dt = rN. In this equation, dN/dt is the growth rate of the population in a given instant, N is population size, t is time, and r is the per capita rate of increase –that is, how quickly the population grows per individual already in the population.
• The integral equation for exponential growth is $N_t=N_0{e}^{r}t$.Where $N_t$=Population density after time t,$N_o$ =Population density at time zero,r=intrinsic rate of natural increase,e=the base of natural logarithms (2.71828),
• So, the correct answer is 'Both A and C'.