Question

In 1980 the population of alligators in a particular region was estimated to be 1800. In 2005 the population had grown to an estimated 5000. Using the Malthusian law for population​ growth, estimate the alligator population in this region in the year 2020.

Answer 1

equation of malthusian model of population growth is of the form P(t)=P_oe^rt, where P_o is initial population , r is growth rate ,t is time

let t be the number of years after the year 1980

t=0 for the year 1980
In 1980 the population was estimated to be 1800
so P_o=1800

=>P(t)=1800e^rt

for the year 2005
t=2005-1980
=>t=25

In 2005 the population had grown to an estimated 5000
=>P(25)=5000
=>1800e^25r=5000

for the year 2020
t=2020-1980
=>t=40

alligator population in this region in the year 2020 is estimated to be 9229

mathematically to roundoff to nearest integer try 9230 also if needed. but 9230^th alligator will not be born in the year 2020