Question

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.

Answer 1

To model the situation of a city with an initial population of 110,000 in 1920, growing at a rate of 1% per year, we can use the exponential growth function:

\[
P(t) = P_0 \cdot (1 + r)^t
\]

where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal), and
- \( t \) is the number of years since the initial population was measured.

Given:
- \( P_0 = 110,000 \)
- \( r = 0.01 \) (which is 1% expressed as a decimal)
- The initial year is 1920, so \( t \) will be the number of years after 1920.

To estimate the population in 1922, we need to calculate \( P(2) \) (since 1922 is 2 years after 1920):

\[
P(2) = 110,000 \cdot (1 + 0.01)^2
\]

Calculating \( (1 + 0.01)^2 \):

\[
(1.01)^2 = 1.0201
\]

Now, substitute it back into the population model:

\[
P(2) = 110,000 \cdot 1.0201 = 112,221
\]

Rounding to the nearest whole number, the estimated population in 1922 is:

\[
\boxed{112221}
\]