Final answer:
The population of the city after decreasing by 2% annually for 15 years is calculated using the exponential decay formula, resulting in an estimated population of approximately 33,337.
Step-by-step explanation:
To calculate the population of a city after it decreases by 2% each year for 15 years, we can use the formula for exponential decay, which is P = P0 × (1 - r)^t, where P is the population after time t, P0 is the initial population, r is the rate of decrease (expressed as a decimal), and t is the time in years.
In this case, the initial population is 45,000, the rate of decrease is 2%, which is 0.02 in decimal form, and the time is 15 years. So, P = 45,000 × (1 - 0.02)^15.
Calculating the population after 15 years:
P = 45,000 × (0.98)^15
P = 45,000 × 0.740818
P ≈ 33,337
So after 15 years, the population is estimated to be approximately 33,337.