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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 ) =

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Answer:

[tex]S(t)=24,000(1.035)^5[/tex]


Step-by-step explanation:

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

[tex]F=P(1+r)^t[/tex]

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, [tex]\frac{3.5}{100}=0.035[/tex])
  • 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:

[tex]S(t)=24,000(1+0.035)^t\\S(t)=24,000(1.035)^t[/tex]

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