Exponential growth problem?

Question

in 1951, the population of India was 357 million people. by 1981 it had grown to 684 million. if the population is growing exponentially, when (in what month of what year) will the population reach 1 billion people?

Answer 1

Population = 357 * b^t

357(1951)=357*b^0

684(1981)=357*b^30

b=(684/357)^(1/30) = 1.02191066

1000=357* 1.02191066 ^ X

(1000/357)=1.02191066 ^ X

(1000/357)^ (1/X) =1.02191066

2.801120448 ^ (1/X) =1.02191066

1/X = Log(1.02191066; base=2.801120448) = 0.021042389

X=1/0.021042389 = 47.5231205

X=47.5231205 years = 1951+ 47.5231205 ≈ 1998.5

47.5231205 - 47 = 0.5231205

365*0.5231205 = 190.938984 days

365/2=182.5 (6 months)

190.938984 - 182.5 = 8.438983985 days

After 6 full month there comes July, thus 1b pop will be in 6-th July in 1998.

♦ Answer: 1 billion population will be reached at 6-th of July in 1998 (close before 11 am if distribution is even)