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Sagot :
Using an exponential function, it is found that the value of David's Investment will be at least $415 after a period of 20 years.
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, the initial value and the growth rate for his investment are given by:
A(0) = 230, r = 0.03.
Hence, the value after t years is given by:
[tex]A(t) = 230(1.03)^t[/tex]
Then, the value will be of at least $415 when:
[tex]A(t) \geq 415[/tex]
[tex]230(1.03)^t \geq 415[/tex]
[tex](1.03)^t \geq \frac{415}{230}[/tex]
[tex]\log{(1.03)^t} \geq \log{\frac{415}{230}}[/tex]
[tex]t\log{1.03} \geq \log{\frac{415}{230}}[/tex]
[tex]t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}[/tex]
[tex]t \geq 20[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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