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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 346 (page 1055)

Coralee invests $$ 5, 000$ in an account that compounds interest monthly and earns $7 %$ . How long will it take for her money to double?

Short Answer

Expert verified

The time taken is $9.9$ years

Step by step solution

01

Given information

Given the investment is $$ 5, 000$ and rate of interest is $7 %$

02

Substitute in the formula for the balance compounded n times

Substituting, we get

$A = P {(1 + \frac{r}{n})}^{n t} 10000 = 5000 {(1 + \frac{0.07}{12})}^{12 t} \frac{10000}{5000} = {(\frac{12.07}{12})}^{12 t} 2 = {(\frac{12.07}{12})}^{12 t} {(\frac{12.07}{12})}^{12 t} = 2$

03

Take logarithm and solve

Taking logarithm, we get

$\log {(\frac{12.07}{12})}^{12 t} = \log 2 12 t \log (\frac{12.07}{12}) = \log 2 t = \frac{\log 2}{12 \log (\frac{12.07}{12})} t 鈮� 9.9$

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Most popular questions from this chapter

In the following exercises, match the graphs to one of the following functions:

$鈸� 2^{x} 鈸� 2^{x + 1} 鈸� 2^{x - 1} 鈸� 2^{x} + 2 鈸� 2^{x} 鈭� 2 鈸� 3^{x}$

Convert from exponential to logarithmic form:

$10^{3} = 1000$ .

In the following exercises, solve each logarithmic equation, $\log_{a} 81 = 2$

In the following exercises, find the inverse of each function.

$f (x) = x^{2} + 6, x 鈮� 0$

In the following exercises, find the inverse of each function.

$f (x) = \frac{x}{4}$

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