Question

The population of retired citizens in Miami is 59,700. If the population decreases at a rate of 2.5% each year, what will the population of retirees be in 4 years?

A) 53,815
B) 54,870
C) 55,925
D) 56,980

Answer 1

Main Answer:

The retired population in Miami will be 55,925 in 4 years due to a 2.5% annual decrease.

Therefore, the correct answer is C) 55,925.

Explanation:

The population decrease can be calculated using the formula: \( \text{Population} = \text{Initial Population} \times (1 - \text{Rate of Decrease})^\text{Number of Years} \). Substituting the given values, we get \( 59,700 \times (1 - 0.025)^4 \approx 55,925 \). This calculation reflects the compounding decrease of 2.5% per year over the 4-year period. The rate of decrease is subtracted from 1 to represent the remaining percentage of the population each year.

Understanding this, the population of retired citizens in Miami is projected to be 55,925 in 4 years. This decrease is influenced by the compounding nature of the annual rate, resulting in a progressively lower population figure each year. It's important to note that this is a mathematical projection based on the given rate and does not account for other factors that might affect the population.

Therefore, the correct answer is C) 55,925.

Answer 2

C) 55,925 because The retired population in Miami will be approximately 55,925 in 4 years due to a 2.5% annual decrease modeled through exponential decay.

Step-by-step explanation:

The population of retired citizens decreases at a rate of 2.5% each year. To calculate the population after 4 years, we can use the formula for exponential decay:

`\[ \text{Final Population} = \text{Initial Population} * (1 - \text{Rate})^{\text{Time}} \]`

In this case, the initial population is 59,700, the rate is 2.5% (or 0.025), and the time is 4 years. Plugging in these values:

`\[ \text{Final Population} = 59,700 * (1 - 0.025)^4 \]`

Calculating this gives us approximately 55,925 retirees. The formula reflects the idea that each year, the population is reduced by 2.5% of the remaining population. Over four years, this compounding effect results in a decrease from the initial 59,700 to the final value of 55,925.

In conclusion, the exponential decay model is an effective way to project population decreases over time, and in this case, it predicts that the retired population in Miami will be around 55,925 in 4 years. This mathematical approach is commonly used in demographic studies and financial analyses to project future values based on known rates of change.