Question

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

Answer 1

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:

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

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

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