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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)=

Ngozi earns $\$ 24,000$ in salary in the first year she works as an interpreter. Each year, she earns a $3.5 \%$ raise. $\newline$ 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. $\newline$ $S(t)=$

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Write exponential functions: word problems

Full solution

Q. Ngozi earns

\$ 24,000

in salary in the first year she works as an interpreter. Each year, she earns a

3.5 \%

raise.

\newline

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.

\newline

S(t)=

Identify Salary and Raise: Identify the initial salary and the annual raise percentage. $\newline$ Ngozi's initial salary is $\$24,000$ , and she receives a $3.5\%$ raise each year.
Convert to Decimal: Convert the annual raise percentage to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $3.5\%$ as a decimal is $3.5 / 100 = 0.035$ .
Write Salary Function: Write the function for Ngozi's salary after $t$ years. $\newline$ Ngozi's salary after $t$ years can be represented by an exponential growth function because she receives a constant percentage raise each year. $\newline$ The general formula for exponential growth is: $\newline$ $\text{Initial amount} \times (1 + \text{growth rate})^{\text{time}}$ $\newline$ So, the function for Ngozi's salary $S(t)$ is: $\newline$ $S(t) = \text{Initial salary} \times (1 + \text{raise rate})^t$
Substitute Initial Values: Substitute the initial salary and the raise rate into the function. $\newline$ $S(t) = 24000 \times (1 + 0.035)^t$ $\newline$ This is the function that represents Ngozi's salary $t$ years after she starts working as an interpreter.

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