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The population growth of a town may be modeled by the regression equation y = 18,000 x 1.04x. which of the following is the best prediction for the population after 30 years?


Sagot :

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.

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