The population of a small town was 3600 in 2005. The population increases by 5% annually. Write an exponential function to represent this situation

To represent the population growth of the small town, we can use the general 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 (expressed as a decimal),
- \( t \) is the number of years since the initial year (2005).

Given:
- Initial population \( P_0 = 3600 \),
- Growth rate \( r = 5\% = 0.05 \),
- \( t \) represents the number of years after 2005.

So, the exponential function representing the population is:

\[
P(t) = 3600 \cdot (1 + 0.05)^t = 3600 \cdot (1.05)^t
\]

This function can now be used to calculate the population at any year \( t \) after 2005.

Would you like further details or any specific examples using this function?

Here are 5 related questions to consider:
1. What will the population be in 10 years (i.e., in 2015)?
2. How long will it take for the population to double?
3. What is the population in 2020?
4. How does this function change if the growth rate was 3% instead of 5%?
5. Can the function model decreasing populations?

**Tip**: Exponential growth functions can also be applied to financial growth, such as investments with compound interest.

The population of a small town was 3600 in 2005. The population increases by 5% annually. Write an exponential function to represent this situation.

Explore how to model population growth with an exponential function. Given a town's population of 3600 in 2005 and a 5% annual increase, this solution demonstrates the exponential growth formula P(t) = 3600 * (1.05)^t. Ideal for high school students learning algebra and functions.

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