A city had a population of 110,000 in 1920. The population grew at a rate of 1% per year thereafter.
Which function could model this situation?
Use the function you selected to estimate the population in 1922.
Round your answer to the nearest whole number.
The function that could model this situation is an exponential function of the form f(x) = a * (1 + r)^x, where a is the initial population, r is the growth rate as a decimal, and x is the number of years.
In this case, the initial population (a) is 110,000 and the growth rate (r) is 1% per year, or 0.01.
Thus, the function that models this situation is f(x) = 110,000 * (1 + 0.01)^x.
To estimate the population in 1922, we need to find the value of x when 1920 + x = 1922.
1920 + x = 1922
x = 2
Plug x = 2 into the function to find the estimated population in 1922:
f(2) = 110,000 * (1 + 0.01)^2
≈ 110,000 * (1.01)^2
≈ 110,000 * 1.0201
≈ 112,211
Rounded to the nearest whole number, the estimated population in 1922 is 112,211. Answer: \boxed{112,211}.