Respuesta :
Using an exponential function, it is found that her total profit for the first ten years is of $422,426.72.
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.
In this problem, we have that the initial value and the growth rate are given as follows:
A(0) = 31124, r = 0.06.
Hence the profit function is given by:
[tex]P(t) = 31124(1.06)^t[/tex]
Then, the total profit over the first 10 years is given by:
[tex]\int_{0}^{10} P(t) dt[/tex]
[tex]\int_{0}^{10} 31124(1.06)^t dt[/tex]
[tex]\frac{31124}{\ln{1.06}} \times (1.06)^t|_{t = 0}^{t = 10} = 422,426.72[/tex]
Thus, her total profit for the first ten years is of $422,426.72.
More can be learned about exponential functions at https://brainly.com/question/25537936
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