Population Growth Model

Question

The population growth model for a particular species of bird has been established as P (t) = P₀e^0.075t

Where P(t) is the population at any time, t, and t is measured in years from 1985, taken as the initial year (t = 0).

If the population was 500 in 1985; in what year will the population double?

Answer 1

P(t) = P₀e^.075t

 

P(t) = 1000 = 500·e^.075t

 

divide both sides by 500

 

2 =e^.075t

 

take ln of both sides

 

ln(2) = ln (e^.075t)

 

.6931 = .075t

 

t = 9.24

 

if the population was 500 at the beginning of 1985, then during the year 1994, the population will double