Question

The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 7 years, how long will it take to triple

Answer 1

Answer:

It will take 11.10 year to triple the population

Step-by-step explanation:

We have given that initial population is $P_0$

It is given that population is doubled in 7 years

So $2P_0=P_0(1+\frac{r}{100})^n$

$2=(1+0.01r)^7$

$1+0.01r=2^{\frac{1}{7}}$

$1+0.01r=1.1040$

$0.01r=0.1040$

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 $=3P_0$

So $3P_0=P_0(1+\frac{10.40}{100})^n$

$3=1.104^n$

Taking log both side

$nlog1.104=log3$

$n\times0.042=0.477$

n = 11.10 year

So it will take 11.10 year to triple the population