Question

One day your boss is griping about how everyone is overpaid and the minimum wage of $7.85 per hour should be lowered. You tell him you will make a deal. Today, for your 8 hour shift, he can pay you just $2 for the first hour, $4 for the second hour, $8 for the third hour and keep doubling until the end of the day. He happily agrees.a. How much do you make for your 8th hour? b. How much do you make for your entire 8 hour shift? c. What is your average hourly pay for the day?

Answer 1

Given that you made this deal for your 8-hour shift:

- He can pay you just $2 for the first hour.

- He can pay you $4 for the second hour.

- He can pay you $8 for the third hour and keep doubling until the end of the day.

a. You can identify that each amount is obtained by multiplying the previous amount by 2.

Therefore, knowing the above, you can find the next five values that correspond to the paid for the fourth hour, the fifth hour, the sixth hour, the seventh hour, and the eighth hour:

`4th\text{ }hour=\text{ \$}8\cdot2=\text{\$}16`
`5th\text{ }hour=\text{ \$}16\cdot2=\text{\$}32`
`6th\text{ }hour=\text{ \$}32\cdot2=\text{\$}64`
`7th\text{ }hour=\text{ \$}64\cdot2=\text{\$}128`
`8th\text{ }hour=\text{ \$}128\cdot2=\text{\$}256`

Now you know how much you make for your 8th hour.

b. In order to calculate how much you make for your entire 8-hour shift, you need to add all the amounts of money that you make each hour:

`\text{ \$}2+\text{\$}4+\text{\$}8+\text{\$}16+\text{\$}32+\text{\$}64+\text{\$}128+\text{\$}256=\text{\$}510`

c. In order to find the average hourly pay for the day, you need to divide the sum found in part "b" by the number of values in the Addition:

`Average=\frac{\text{ \$}510}{8}=\text{\$}63.75`

Hence, the answers are:

a.

`\text{ \$}256`

b.

`\text{\$}510`

c.

`\text{\$}63.75`