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Rhonda started a business. Her business made $30,000 in profits the first year. Her annual profits have increased by an average 5% each year since then.


A) Write an iterative rule to model the sequence formed by profits of Rhonda’s business each year.


B) Use the rule to determine the annual profits of Rhonda’s business can be predicted to be 15 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end, show your work.

Respuesta :

Using an exponential function, it is found that:

a) The model is: [tex]A(t) = 30000(1.05)^t[/tex]

b) Her predicted profit is of $62,368.

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.

Item a:

  • $30,000 in profits on the first year, hence [tex]A(0) = 30000[/tex].
  • Grows 5% each year, hnce [tex]r = 0.05[/tex]

Then:

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

[tex]A(t) = 30000(1 + 0.05)^t[/tex]

[tex]A(t) = 30000(1.05)^t[/tex]

Item b:

[tex]A(15) = 30000(1.05)^{15} = 62368[/tex]

Her predicted profit is of $62,368.

For more on exponential functions, you can check https://brainly.com/question/25537936

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