Question

9)
The rate of growth of population is
proporational to the number present.
If the population doubled in the last 25 years
and the present population is 1 lac, when
will the city have population 4,000,000?
I want serious answer not a fake one or I will report it​

Answer 1

Step-by-step explanation:

dt

dp

∝p

⟹

dt

dp

=kp (where k is constant)

⟹∫

dt

dp

=∫kdt

⟹lnp=kt+c (on integrating both sides)

At t=0,p=(1/2)lac=50,000.

At t=25,p=(1/2)lac=1,00,000.

∴ we get, c=ln(50,000) and k=ln(2)/25

∴ For P=4,00,000

lnp=

25

ln(2)

t+ln(50,000)

ln(4,00,000)=

25

ln(2)

t+ln(50,000)

Solving for t, we get t=75.

Now as we have assumed t=0 after 25 years. So, city have population of 4,00,000 before 25 years.

Hence time =75−25=50years

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