Question

Help please !
a country's population in 1992 was 39 million. In 1997 it was 42 million. Estimate the population in 2009 using the exponential growth formula

Answer 1

Xt = Xo (1+r)^t

Xt = population at time t
Xo = population at time 0
t = time
r = rate.

At 1992,
39 = Xo (1+r)^1992 ------(1)

At 1997
42 = Xo (1+r)^1997 -------- (2)

(1) / (2):

39/42 = (1+r)^(1992-1997)
39/42 = (1+r)^(-5)
39/42 = 1 / (1+r)^5
(1+r)^5 = 42 / 39
(1+r) = root5 (42/39)
r = root5(42/39) -1
r = 0.014931978

Thus,
42 = Xo (1+0.014931978)^1997
Xo = 5.870657669 x 10^-12

At 2009,
X2009 = (5.870657669X10^-12) (1+0.014931978)^2009
X2009 = 50.17669491 MILLION

Answer 2

thanks !!!!