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The image presents a mathematical problem related to the average annual salary of an Ohio employee, with the salary modeled by a function of time. The formula given in the problem is:

\[
A = 48,034 \times (1 + 0.031)^t
\]

where:
- $ A $ represents the average annual salary,
- $ t $ represents the time in years since 2010,
- 0.031 is the annual growth rate.

The questions in the problem ask for:

### a. **Initial Value and Growth Rate**
1. The **initial value** (in dollars) and its practical meaning.
2. The **growth rate** (as a percentage) and its practical meaning.

### b. **Estimate Average Salary in 2025** 
You need to use the formula to estimate the average salary for 2025. Since 2025 is 15 years after 2010 ($ t = 15 $), you would plug this value into the formula.

### c. **Find the Year When Salary Reaches $89,437**
This part asks you to determine the year when the average salary will reach at least $89,437. To solve this, you need to solve the equation for $ t $:

\[
89,437 = 48,034 \times (1 + 0.031)^t
\]

Would you like me to walk you through each part of the solution in more detail?

Here are 5 questions related to this information:
1. What is the formula for calculating the initial value from an exponential growth equation?
2. How does the growth rate affect the value of $ A $ over time?
3. Why do we use logarithms to solve for $ t $ in part (c)?
4. How would the result change if the growth rate were higher or lower than 3.1%?
5. What is the significance of knowing the average salary for a specific year like 2025?

**Tip:** When solving exponential equations, logarithms are essential for isolating the exponent.

Suppose the average annual salary in dollars, A, of an Ohio employee is a function of the time in years since 2010, t. An approximate formula is A = 48,034 * (1 + 0.031)^t. Identify the initial value and growth rate of the function, estimate the salary in 2025, and find the year when the salary reaches at least $89,437.

Learn how to analyze an exponential growth function representing the average salary of an Ohio employee. This problem covers the identification of initial values, the growth rate, and estimates future salaries. Find out when the salary will reach $89,437 using logarithms.

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