75peoplex340 years =2000000 people.how much is 2 mill.x 340 years at the same rate of increase in population.?

Question

75 people increase to 2 million in 430 years

Answer 1

If people increase in geometric progression with a common ratio of r per year, startinmg with a people, the number of people after n years is ar^(n–1) (standard formula for a geometric progression).

In your problem the only thing that changes is the number of people you start with, a. Since r and n are unchanged, you can just scale up the result.

If 75 people grow to 2,000,000 people in 340 years, then at the same rate of growth 2,000,000 people will grow to 2,000,000 x 2,000,000 / 75 = 53 billion approx.

Quite a lot.

Answer 2

No. - Starting Population.
N - Population.
R - Number factor.
t - time factor.
N = No.e^RT

First calculate the R value.
N = No.e^RT
N/No. = e^RT (take logs).
Ln (N /No.) = RT
R = Ln (N /No.) / T
R = Ln (2*10^6 /75) / 340
R = 10∙191 169 62 / 340
R = 0∙029 974 028

Now calculate the new population.
N = No.e^RT
N = (2*10^6)e^(0∙029 974 028)(340)
N = (2*10^6)e^10∙191....
N = (2*10^6)(26,666∙66...)
N = 5∙33...*10^10
N = 53,333∙33... Million People.