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:
\[ \boxed{112221} \]
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