Question

A city is growing at the rate of 0.4% annually. If there were 3,673,000 residents in the city in 1993, find how many (to the nearest ten thousand are living in that city in 2000. Use y=3,673,000(2.7)^0.004t

A. 9,920,000
B. 3,810,000
C. 3,780,000
D. 280,000​

Answer 1

Using the corrected exponential growth formula, the population of the city in 2000, growing at an annual rate of 0.4%, is approximately 3,780,000 (option c) when rounded to the nearest ten thousand.

Step-by-step explanation:

To find the population in the city in the year 2000, we need to apply the exponential growth formula. The formula for exponential growth is y = P(1 + r)^t, where P is the initial population, r is the growth rate, and t is the time in years.

The mistake in the formula given in the question is the presence of 2.7, which should be replaced with the proper growth factor 1.004 for a 0.4% growth rate. Therefore, the corrected formula is y = 3,673,000 * (1.004)^t with t being 7 years since we're interested in the population from 1993 to 2000.

Calculating this, we get y = 3,673,000 * (1.004)⁷. This gives us y = 3,673,000 * 1.028, which results in a population of approximately 3,777,924. Rounding to the nearest ten thousand, we get a population of 3,780,000.