Question

Ngozi earns $24,000 in salary in the first year as an interpreter, with a 3.5% raise each year. Write a function S(t) that gives Ngozi's salary in dollars t years after she starts working.

Answer 1

Ngozi's salary function for t years after she starts working is represented by S(t) = 24,000 × (1 + 0.035)^t, reflecting her starting salary and a 3.5% compounded annual raise.

Step-by-step explanation:

The function that represents Ngozi's salary t years after she starts working is S(t) = 24,000 × (1 + 0.035)t. To create this function, we start with her initial salary of $24,000 and apply a 3.5% raise each year.

The raise is compounded annually, which is why the raise factor, 1 + 0.035 (or 1.035), is raised to the power of t, representing the number of years since she started.

This function enables the calculation of Ngozi's evolving salary over time, offering a dynamic model for financial projections. As t increases, S(t) yields the corresponding salary, reflecting the incremental growth due to the annual raise, crucial for long-term salary planning and financial forecasting.

Each year, the salary is multiplied by this factor to account for the annual increase. Therefore, after t years, her salary is the original amount multiplied by the raise factor to the power of t to reflect each year's compounded raise.