Answer
a) 160000 people
b) 33rd year
Work Step by Step
a) Follow the Malthusian Growth Model:
$P(t)=P_0e^{kt}$
And the the doubling time is:
$t_d=\frac{1}{k} \ln 2$
The population of the city was 10,000 and by 2005 it had
risen to 20,000. We can say $t_d=5$
Substituting to solve for $k$:
$5=\frac{1}{k} \ln 2$
$k=0.139$
Substituting $k$ for the Malthusian Growth Model and find the population at $t=20$:
$P(t)=10000e^{0.139.20}$
$P(t)=160000$
b) Now find the year that the population will reach one million:
$1000000=10000e^{0.139t}$
$e^{0.139t}=100$
$\rightarrow t=33.21$
Thus, the population will reach one million in the 33rd year.
