The population of a town has approximately doubled every 17 years since 1950.
the equation P=[tex]P_02^k[/tex] where Po is the population of the town in 1950, is used to model the population, P, of the town t years after 1950.
When t=17 yrs
P=2[tex]p_{0}[/tex]
for 1 year
The equation becomes
P = [tex]P_02^\frac{t}{17}[/tex] -------------(1)
Our original equation is
[tex]P=P_02^k[/tex]----------------------------------(2)
equating expression 1 and 2
[tex]P_02^\frac{t}{17}=P_{0}2^k[/tex]
Cancelling [tex]P_{0}[/tex] from both sides we get
[tex]2^\frac{t}{17}=2^{k}[/tex]
t/17=k
⇒k=t/17 is the solution.
