Question

The population of a certain community is increasing at a rate directly proportional to the population at any time t. In the last 7 years, the population has doubled. How long will it take for the population to triple?

Answer 1

Answer:

11.08 years

Step-by-step explanation:

Given that the  population of a certain community is increasing at a rate directly proportional to the population at any time t.

i.e. $\frac{dP}{dt} = kP$

Separate the variable and integrate to get

ln P = k t +C

$P(t) = Ae^{kt}$

When t=0 initial population =A

When t=7, P has become 2A

$Ae^{7t } =2A\\7t=ln 2 \\t = 0.099$

Hence equation is

$P(t)=Ae^{0.099t}$

When tripled we get

$Ae^{0.099t}=3A\\t =11.09709$