Question

A population of certain town is 1,25,000. if the annual birth rate is 3.3% and the annual death rate is 1.3%, then the population after 3 years is

Answer 1

Given Population P = 125000, n = 3 years, R = (3.3 - 1.3) = 2%.

Now,

Population after 3 years is:

= > A = P(1 + r/100)^n

= > 125000(1 + 2/100)^3

= > 125000(102/100)^3

= > 125000(51/50)^3

= > 132651.

Therefore, the population after 3 years = 132651.

Hope this helps!

Answer 2

annual birth rate , $r_1$ = 3.3%
annual death rate, $r_2$ = 1.3 %
So, net birth rate , R = $r_1-r_2$
R = 3.3 % - 1.3 % = 2%

because population increases in geometric progression. so, we have to use similar formula of compound interest.
Let A is the population after 3 years .
n is the time period
R is the net birth rate.
P is the population of town initially

so, $A=P(1 + \frac{R}{100})^n$
A = 1,25,000(1 + 2/100)³
A = 1,25,000(1 + 0.02)³
A = 1,25,000 × (1.02)³
A = 1,32, 651

hence, population after 3 yrs = 1,32,651