Question

Ngozi earns $ 2 4 , 0 0 0 $24,000 in salary in the first year she works as an interpreter. Each year, she earns a 3 . 5 % 3.5% raise. Write a function that gives Ngozi's salary S ( t ) S(t), in dollars, t t years after she starts to work as an interpreter. Do not enter commas in your answer. S ( t ) =

Answer 1

`S(t)=24,000(1.035)^5`

Explanation:

This is a compound growth problem. The general formula for compound growth can be written as:

`F=P(1+r)^t`

Where

• F is the future amount, or the function (in our case it's S(t), which is Ngozi's salary after t years)
• P is the initial amount (first year salary is 24,000 so that the initial amount)
• r is the rate of growth (3.5% raise, or growth each year. In decimal,
  `(3.5)/(100)=0.035`)
• t is the time in years (we will leave t as t, because it didn't ask for any specific amount of years)

Now we can write the equation as:

`S(t)=24,000(1+0.035)^t\\S(t)=24,000(1.035)^t`