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^(t)/(17)` -------------(1)

Our original equation is

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

equating expression 1 and 2

`P_02^(t)/(17)=P_(0)2^k`

Cancelling
`P_(0)` from both sides we get

`2^(t)/(17)=2^(k)`

t/17=k

⇒k=t/17 is the solution.