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David invested $230 in a savings account that offers a 3% return on the Investment. The value of David's Investment will be at least $415 after a
period of
years.
Hint: Use the formula A= P1+, where A is the amount after tyears, Pls the amount Invested, r is the rate of interest, and t is the time period.
Use a calculator to compute the answer, and round It off to the nearest year.
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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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