It took roughly 200000 years for the human population to rea

It took roughly 200,000 years for the human population to reach its first billion. Assuming an initial population size of 1,000 calculate r over the first 200,000 years.

I am assuming that we use the N_t=e^r*t*N₀ to solve with N_t being the population size after the 200,000 years (1,000,000,000), t being 200,000 and N₀ being the initial population size of 1,000.

Solution

The exponential population growth formula is, Nt = N0 e^rt

Where, Nt = population after t time

N0 = Initial population size

r = growth rate

t = time in years = 200 000 years

Thus,

1,000,000,000 = 1,000* e^r*200,000

Thus, the growth rate, r = 6.90775527898e-05 = 0.00690775527898%