Let P be the population of some geographical area. If the population of the area changes over time based on...

Question

Let P be the population of some geographical area. If the population of the area changes over time based on the following criteria, which of them signals exponential growth of the population?

 

I. The change in population is directly proportional to itself.

II. The change of population is inversely proportional to itself.

III. The change of population is directly proportional to e^population.

 

Possible answers include:

 

A. I only

B. I and II only

C. II and III only

D. I and III only

Answer 1

Exponential growth would be: P=P₀e^kt, which gives

P'=kP₀e^kt or  P'=kP  (not P'=k/P or P'=ke^P).