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The given function models the population of a town:

\[
P(t) = 12.5(1.04)^t
\]

This is an exponential growth model where:

- \( P(t) \) is the population in thousands, after \( t \) years.
- The factor \( 1.04 \) represents the annual growth rate of the population.

The general form of an exponential growth equation is:

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

where:
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.

In this case, comparing the given function to the general form, we can see that the growth factor \( 1.04 \) corresponds to \( 1 + r \). Thus:

\[
1 + r = 1.04
\]

Solving for \( r \):

\[
r = 1.04 - 1 = 0.04
\]

To convert this growth rate to a percentage, multiply by 100:

\[
r = 0.04 \times 100 = 4\%
\]

Therefore, the population is expected to grow by **4% each year**, which corresponds to option **C)**.

Would you like further details or have any questions? 

Here are 5 related questions to consider:
1. What is the general form of exponential decay, and how is it different from growth?
2. If the population growth rate changed to 6%, what would the new growth factor be?
3. How would the population be affected if the growth rate were negative, representing a decline?
4. How do you calculate the doubling time of a population with a 4% growth rate?
5. Can you model population growth with a continuous compounding function?

**Tip:** Exponential models are commonly used to describe not only population growth but also things like investments and radioactive decay. Keep an eye on the growth/decay factor when interpreting these models!

The given function models the population, in thousands, of a town t years from now. According to the model, by what percent is the population expected to grow each year?

Solve an exponential growth model problem to find the population growth rate. Learn how to interpret and apply the exponential growth formula, P(t) = 12.5(1.04)^t, to determine the annual growth rate. Suitable for high school math students.

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