Question

The population of a city was 400,000 in 1995. The population has grown at a rate of 3% each year since then. Choose the equation that could be used to find the number of years after 1995 it will take for the city to reach a population of 950,000 if the growth rate remains the same.

A. 400,000(1.03)^x=950,000
B. 400,000+3x=950,000
C. 400,000(x)^3=950,000
D. 400,000+3^x=950,000

Answer 1

The correct equation to determine the number of years it will take for a city's population to grow from 400,000 to 950,000 with a growth rate of 3% annually is A. 400,000(1.03)^x = 950,000.

Step-by-step explanation:

The question involves finding the number of years it will take for a city's population to grow from 400,000 to 950,000, given a constant growth rate of 3% annually. To solve problems involving exponential growth, we use the formula P = P0(1 + r)^t, where P is the future population, P0 is the initial population, r is the rate of growth, and t is the time in years. The correct equation that represents this situation is A. 400,000(1.03)^x = 950,000. This equation reflects exponential growth because each year, the population is multiplied by 1.03 (the 3% growth rate).