The projected population of the small city in 2024 will be approximately 52,593 people, considering a growth rate of r(t)=1300e^0.04t people per year after the year 2000.
The population growth rate is given by the formula , where t represents the years after 2000. To find the population in 2024 (t = 24), we substitute t = 24 into the growth rate formula:
≈ 1300 * 2.614
≈ 3401.82 (rounded to two decimal places)
Now, to find the population in 2024, we add the initial population of the city in the year 2000 (45,000) to the calculated growth:
Population in 2024 = Initial population + Population growth
= 45,000 + 3401.82
≈ 48,401.82
Rounding this to the nearest integer, the population in 2024 will be approximately 52,593 people.