Chapter 1.2, Problem 103E

To determine

To find: the number of years would it take to use all the money and the number of years would it take to empty a suitcase filled with a billion $\left({10}^9\right)$ dollars.

Answer to Problem 103E

One million dollars were spent in $2.74\text{years}$ .

One billion dollars were spent in $2739.726\text{years}$ .

Explanation of Solution

Given information:

If you had a million $\left({10}^6\right)$ dollars in a suitcase, and you spent a thousand $\left({10}^3\right)$ dollars each day.

Calculation:

The amount in a suitcase $=\${10}^6$

Amount spends for a day $=\${10}^3$

Number of days to spend total money

  $\begin{array}{c}\frac{{10}^6}{{10}^3}={10}^{6-3}\text{by}\text{using}\text{the}\text{quotient}\text{rule},\frac{a^m}{a^n}=a^{m-n}\\ ={10}^3\\ =1000\text{days}\end{array}$

Number of days per year $=365$

Number of years

  $\frac{1000}{365}=2.74\text{years}$

Therefore, one million dollars were spent in $2.74\text{years}$ .

If the amount in suitcase is $\${10}^9$

Number of days to spend total money

  $\begin{array}{c}\frac{{10}^9}{{10}^3}={10}^{9-3}\text{by}\text{using}\text{the}\text{quotient}\text{rule},\frac{a^m}{a^n}=a^{m-n0}\\ ={10}^6\\ =1000000\text{days}\end{array}$

Number of days per year $=365$

Number of years

  $\frac{1000000}{365}=2739.726\text{years}$

Therefore, one billion dollars were spent in $2739.726\text{years}$ .