Question

Ngozi earns
\[\$24{,}000\] in salary in the first year she works as an interpreter. Each year, she earns a
\[3.5\%\] raise.
Write a function that gives Ngozi's salary
\[S(t)\], in dollars,
\[t\] years after she starts to work as an interpreter.
Do not enter commas in your answer.
\[S(t)=\]

Answer 1

To represent Ngozi's salary as a function of the number of years worked, we can use the concept of geometric growth due to the annual percentage raise.

Given:
- Initial salary, \( S(0) = 24000 \)
- Annual raise rate = 3.5% = 0.035

In the first year, her salary is \( 24000 \). In the second year, she will earn \( 24000 \times (1 + 0.035) \), and this pattern continues each year.

The general formula for her salary after \( t \) years will be:
\[
S(t) = S(0) \times (1 + r)^t
\]
where \( r \) is the raise rate.

Substituting the known values:
\[
S(t) = 24000 \times (1 + 0.035)^t
\]
\[
S(t) = 24000 \times (1.035)^t
\]

Therefore, the function that gives Ngozi's salary \( S(t) \), in dollars, \( t \) years after she starts to work as an interpreter is:
\[
S(t) = 24000(1.035)^t
\]