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growth: Word problems V84
Kenny lives in Greenpoint, where the cost of living increases by 8% every year. If Kenny
spends $50,700 this year, how much can he expect to spend 11 years from now to maintain
the same standard of living?
If necessary, round your answer to the nearest cent.

Respuesta :

Using an exponential function, it is found that he must spend $118,214 in 11 years to keep the same standard of living.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the growth rate, as a decimal.

His current cost of living is of $50,700, which increases by 8% yearly, hence A(0) = 50700, r = 0.08, and the equation is:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 50700(1 + 0.08)^t[/tex]

[tex]A(t) = 50700(1.08)^t[/tex]

After 11 years, the cost will be given by:

[tex]A(11) = 50700(1.08)^{11} = 118214[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

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