Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A historian is analyzing population data. The population of a city was 250,000 in the year 2000. If the population grew at an average rate of 3% per year, approximately what would be the population in the year 2005?
- A265,000
- B281,377
- C297,500
- D289,819
Show answer & explanationAnswer & explanation
Correct answer: D. 289,819
This problem involves compound growth. The population after 'n' years can be calculated using the formula: Initial Population * (1 + rate)^n. Here, n = 2005 - 2000 = 5 years.
Why the other options are wrong
- A. This is the result of simple interest (250,000 + 250,000 * 0.03 * 5), not compound growth.
- B. This is a plausible distractor from a calculation error.
- C. This is a plausible distractor, perhaps from incorrect exponentiation or rounding.
Compound Growth
Compound growth occurs when a quantity increases by a certain percentage over a period, and that percentage is then applied to the new, larger quantity in the next period. It is calculated with the formula P(1+r)^n.
- Growth is applied to the accumulated total, not just the initial amount.
- Formula: Future Value = Present Value * (1 + rate)^time.
- Used for population growth, compound interest, inflation.
Memory trick: Growth that keeps growing on top of itself, year after year.