The population of a city was 50000 in 1950 and 70000 in 1960

5. The population of a city was 50,000 in 1950 and 70,000 in 1960. Assuming exponential growth, when did the population reach 100,000?

Solution

Solution:

Initial Population = 50,000

after 10 year it becomes 70,000

therefore

A (10) = A_oe^kt

70000 = 50000 e^k*10

e^k*10 = 7/5

k = 0.0336

Now

we have to calculate time when population 100000

A = 100000

100000 = 50000 e^kt

2 = e0.0336t

t = 20.629 = 20.63 years

therefore

20.63 years later 1950 population reaches to 100,000

Answer