Answer:
It will take 11.10 year to triple the population
Step-by-step explanation:
We have given that initial population is [tex]P_0[/tex]
It is given that population is doubled in 7 years
So [tex]2P_0=P_0(1+\frac{r}{100})^n[/tex]
[tex]2=(1+0.01r)^7[/tex]
[tex]1+0.01r=2^{\frac{1}{7}}[/tex]
[tex]1+0.01r=1.1040[/tex]
[tex]0.01r=0.1040[/tex]
r = 10.40 %
So rate of increasing the population will be 10.40 %
Now we have to find the time in which population is 3 times
So new population [tex]=3P_0[/tex]
So [tex]3P_0=P_0(1+\frac{10.40}{100})^n[/tex]
[tex]3=1.104^n[/tex]
Taking log both side
[tex]nlog1.104=log3[/tex]
[tex]n\times0.042=0.477[/tex]
n = 11.10 year
So it will take 11.10 year to triple the population
