Question

Suppose a certain country's population has constant relative birth and death rates of 97 births per thousand people per year and 47 deaths per thousand people per year respectively. Assume also that approximately 30,000 people emigrate (leave) from the country every year. Which equation best models the population P- Pt) of the country, where t is in years? dP - 50P30000 Oat 30000 dit d0.05P30000 it 0.5P30000 dP 0.5P 30 ait

Answer 1

The best equation to model the population P(t) considering birth rates, death rates, and emigration is dP/dt = 0.05P - 30000.

Step-by-step explanation:

To model the population P(t) of a country with constant relative birth and death rates, alongside a constant number of people emigrating each year, we employ the demographic equation. The equation accounts for births, deaths, and migration to find the net population change.

The birth rate is 97 births per thousand people per year, which translates to a rate of 0.097 when expressed as a proportion (97/1000). Similarly, the death rate is 47 deaths per thousand people per year, corresponding to a rate of 0.047. Emigration is a flat number of 30,000 people per year.

To find the net growth rate, subtract the death rate from the birth rate: 0.097 - 0.047 = 0.05 (or 5% per year). Since we have a constant number of people emigrating, we must subtract this from the overall growth in terms of the population size. That would give us the equation dP/dt = 0.05P - 30000, which models the population P(t) over time t.