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. [tex]\frac{dP}{dt} = kP[/tex]
Separate the variable and integrate to get
ln P = k t +C
[tex]P(t) = Ae^{kt}[/tex]
When t=0 initial population =A
When t=7, P has become 2A
[tex]Ae^{7t } =2A\\7t=ln 2 \\t = 0.099[/tex]
Hence equation is
[tex]P(t)=Ae^{0.099t}[/tex]
When tripled we get
[tex]Ae^{0.099t}=3A\\t =11.09709[/tex]
