Question

A particular city had a population of 26,000 in 1940 and a population of 33,000 in 1980. Assuming that its population continues to grow exponentially at a constant rate, what population will it have in 2000? The population of the city in 2000 will be people (Round the final answer to the nearest whole number as needed Round all intermediate values to sax decimal places as needed)

Answer 1

To predict the city's population in 2000, we solve for the exponential growth rate based on the population data from 1940 and 1980. We can then use this growth rate to predict the population in 2000, which approximates to about 48,194.

Step-by-step explanation:

To solve this problem, we need to use the formula for exponential growth: P = P0 * ekt, where P is the final population, P0 is the initial population, k is the growth rate, and t is the time that has passed.

From the given data, we have P0 = 26,000 (1940's population), P = 33,000 (1980's population) and t = 1980 - 1940 = 40 years.

First, we solve for k using these data points.

33,000 = 26,000 * e40k

1.26923 = e40k

ln(1.26923) = 40 * k

k = ln(1.26923) / 40 = 0.00575

Now, to predict the population in 2000, we substitute t = 2000 - 1940 = 60 years and k = 0.00575 into the formula.

P = 26,000 * e0.00575 * 60

P = approximately 48,194 (rounding to the nearest whole number).

Therefore, expected population of the city in 2000 would be about 48,194.

Learn more about exponential growth