Question

You have a part-time job. One day your boss offers to pay you either 2h−1 or 2h − 1 dollars for each hour h you work that day. Complete the table. Which option should you choose? Explain.

I filled in the first part of the table I just need help on the second part.

Answer 1

For the second part, you have to subtract 1 from the number of hours and raise it to that power.

For example, when h = 1, you have:

2^(1 - 1)
2^0
1

The 5 values in your table would be:
1 2 4 8 16

Answer 2

The better option is
`2^h -1` hour every h hour, because in this way, we can earn more.

Explanation:

We are given the following information in the question:

On a part time job, a person is paid
`2^(h-1)` for every hour h he works.

Then payment can be written as:

`h = 1, 2^(h-1) = 2^(1-1) = 2^0 = 1\\h = 2, 2^(h-1) = 2^(2-1) = 2^1 = 2\\h = 3, 2^(h-1) = 2^(3-1) = 2^2 = 4\\h = 4, 2^(h-1) = 2^(4-1) = 2^3 = 8\\h = 5, 2^(h-1) = 2^(5-1) = 2^4 = 16`

Table:

h: 1 2 3 4 5

Pay: 1 2 4 8 16

The better option is
`2^h -1` hour every h hour, because in this way, we can earn more.