Your starting annual salary of \( \$ 69,000 \) increases by \( 4 \% \) each year a) Write the exponential function. b) What will be your annual salary in 10 years? Round your answer to the nearest dollar.

Let's address each part of your question step-by-step. ### **a) Exponential Function** The exponential function to model your annual salary increase can be written as: \[ S(t) = 69,\!000 \times (1.04)^t \] - **\( S(t) \)**: Salary after \( t \) years - **\( 69,\!000 \)**: Starting annual salary in dollars - **\( 1.04 \)**: Growth factor (4% increase each year) - **\( t \)**: Number of years ### **b) Annual Salary in 10 Years** To find your annual salary after 10 years, plug \( t = 10 \) into the exponential function: \[ S(10) = 69,\!000 \times (1.04)^{10} \] First, calculate \( (1.04)^{10} \): \[ (1.04)^{10} \approx 1.480244 \] Now multiply this by the starting salary: \[ S(10) = 69,\!000 \times 1.480244 \approx 102,\!137 \] **Your estimated annual salary in 10 years will be approximately \$102,137.** --- **Final Answers:** **a)** The exponential function is \( S(t) = 69,\!000 \times (1.04)^t \). **b)** The annual salary in 10 years will be approximately \$102,137.