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gregori [183]
1 year ago
12

Type the correct answer in the box. Use numerals Instead of words. If necessary, use / for the fraction bar.

Mathematics
1 answer:
Zielflug [23.3K]1 year ago
4 0

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.

<h3>What is an exponential function?</h3>

An increasing exponential function is modeled by:

A(t) = A(0)(1 + r)^t

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:

A(t) = 230(1.03)^t

Then, the value will be of at least $415 when:

A(t) \geq 415

230(1.03)^t \geq 415

(1.03)^t \geq \frac{415}{230}

\log{(1.03)^t} \geq \log{\frac{415}{230}}

t\log{1.03} \geq \log{\frac{415}{230}}

t \geq \frac{\log{\frac{415}{230}}}{\log{1.03}}

t \geq 20

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

#SPJ1

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