Question

if the population growth rate of a city in Nepal has 4%after how many years the population of the city will be doubled​

Answer 1

Answer:

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

Answer 2

Answer:

100÷4

.= 25

so answer is 25 years