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Step-by-step explanation:
To find the population of the town after 30 years using the given regression equation, we need to interpret the equation correctly. The equation provided seems to be in a format for exponential growth, but it lacks the correct form. The typical form of an exponential growth equation is:
\[ y = y_0 \times (1 + r)^t \]
Where:
- \( y \) is the population at time \( t \).
- \( y_0 \) is the initial population.
- \( r \) is the growth rate.
- \( t \) is the time in years.
Given:
- \( y_0 = 18,000 \)
- \( r = 0.04 \) (which corresponds to a 4% growth rate per year)
- \( t = 30 \) years
The equation should be:
\[ y = 18,000 \times (1.04)^{30} \]
We can calculate this as follows:
\[ y = 18,000 \times (1.04)^{30} \]
Using a calculator or software for precise computation:
\[ (1.04)^{30} \approx 3.2434 \]
So,
\[ y \approx 18,000 \times 3.2434 \]
\[ y \approx 58,381.2 \]
Therefore, the best prediction for the population after 30 years is approximately 58,381.