Question

Determine the expected population for a rural community of 1,500 people after 15 years if the community is losing population at a rate of 1%/y because of migration to urban areas. The birth rate is 20 per thousand per year and the death rate is 0.5 percent per year.

Answer 1

Answer: Expected population of the rural community after 15 years = 10819

We can determine the expected population of the rural community by the equation :

N_t = N₀ e^rt

where

N_t = Population after time t ( here t = 15 years)

N₀ = Population at time zero (here 1500 people)

r = intrinsic rate of natural increase

e = the base of natural logarithms (2.71828)

r, can be arrived at by :

Let the births be b = 20 per thousand, (30 for 1500)

let deaths be d = 0.5 % per year (7.5 for 1500)

Let migration be E = 1% per year (15 for 1500)

so r = 30 - (7.5 +15) = 7.5

Substituting the values,

N_{(15 years)} = 1500 (2.71828)^{7.5 * 15}

   = 10819.

So, expected population after 15 years is = 10819.