3 The exponential model below represents the population of a town \( x \) years from now. What is meaning of 10581 in the model? \( f(x)=10881(1.03)^{x} \) Show your work here Hint To add an exponent \( \left(x^{\prime \prime}\right) \), type "exponent" or press " \( \wedge \) ". O The town will have doubled in population after 10881 years O Every year, the town decreases in population by 10881 O The town's the town increases in population by 10881 O The town's population will be zero after 10881 years

In the exponential model \( f(x) = 10881(1.03)^x \), each component has a specific meaning: - **10881**: This is the initial population of the town when \( x = 0 \) years. - **1.03**: This represents the growth factor, indicating a 3% increase in population each year. - **\( x \)**: The number of years from now. **Interpretation of 10881:** The number **10881** is the population of the town at the starting point of the model, which is \( x = 0 \) years. It signifies that currently, or at the initial time, the town has a population of **10,881** people. **Evaluating the Options:** 1. **The town will have doubled in population after 10881 years.** - *Incorrect.* The doubling time is based on the growth rate, not directly on the initial population. 2. **Every year, the town decreases in population by 10881.** - *Incorrect.* The model shows growth, not a decrease. 3. **The town increases in population by 10881.** - *Incorrect as phrased.* More accurately, **10881** is the starting population, not the amount it increases by each year. 4. **The town's population will be zero after 10881 years.** - *Incorrect.* The population is growing exponentially, not declining to zero. **Closest Correct Interpretation:** While none of the options perfectly describe the role of **10881**, the most accurate understanding is that **10881** represents the **initial population** of the town at the present time. **Correct Option:** > **The town's the town increases in population by 10881** *However, it's important to note that the phrasing of the options could be improved for clarity. The number **10881** specifically refers to the initial population, not the annual increase.*