Question

The population of a city in Alabama increases every year by 11.5 percent. If the population in 2011 was 4.8 million, what will its population be in 2016? A. 2.6 million B. 2.76 million C. 8.27 million D. 220 million

Answer 1

Using the compound growth formula, the population of the city in Alabama in 2016 with an 11.5% annual increase starting from 4.8 million in 2011 is approximately 8.27 million.

Step-by-step explanation:

To calculate the population of a city in Alabama in 2016 given the annual increase rate of 11.5% and the 2011 population of 4.8 million, we use the formula for compound growth:

P = P0 * (1 + r)^t

Where:

• P is the future population,
• P0 is the initial population,
• r is the growth rate per period,
• t is the number of periods.

By substituting the given values:

P = 4.8 million * (1 + 0.115)^5

Calculating this gives:

P ≈ 4.8 million * (1.718)

P ≈ 8.247 million

Therefore, the closest population estimate for the city in 2016 would be 8.27 million (Choice C).