Final answer:
The approximate population of a city that will quadruple in 15 years, with a current population of 6,000, will be calculated based on the annual growth rate and applying it over 7 years, then rounding to the nearest hundred.
Step-by-step explanation:
The question asks us to calculate the approximate population of a city in 7 years, given that it will quadruple in 15 years and its current population is 6,000. To solve this, we first need to find the annual growth rate that would result in the population quadrupling in 15 years.
To find the annual growth rate (r), we can use the formula for exponential growth P = P0 (1 + r)^t, where P is the final population, P0 is the initial population, and t is the time in years. We know that the city's population will be 4 times the current population (P = 4 × 6000) in 15 years (t = 15).
Solving for r in the formula, we get r = (4^(1/15)) - 1. Then we can calculate the population in 7 years by replacing the value of t with 7 and using the growth rate we found to compute P = 6000 (1 + r)^7. By rounding to the nearest hundred, we obtain the approximate population after 7 years.
Calculation Details:
- Find the annual growth rate: r = (4^(1/15)) - 1.
- Calculate the population in 7 years: P = 6000 × (1 + r)^7.
- Round the result to the nearest hundred.