Question

The population of a town has approximately doubled every 17 years since 1950. If the equation P=Po2k, where Po is the population of the town in 1950, is used to model the population, P, of the town t years after 1950, what is the value of k?

Answer 1

The population of a town has approximately doubled every 17 years since 1950.

the equation P=$P_02^k$ 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$p_{0}$      

for 1 year

The equation becomes

P = $P_02^\frac{t}{17}$                               -------------(1)

Our original equation is

$P=P_02^k$----------------------------------(2)

equating expression 1  and 2

$P_02^\frac{t}{17}=P_{0}2^k$

Cancelling $P_{0}$  from both sides  we get

$2^\frac{t}{17}=2^{k}$

t/17=k

⇒k=t/17 is the solution.