Question

You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?

Answer 1

y=3^x

Explanation:

The expected payments (in cents) beginning from July 1 are given below:

`3,9,27,81,\cdots`

Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.

We can rewrite the payment as a power of 3 as follows:

`3^1,3^2,3^3,3^4,\cdots`

Therefore, the equation will help you determine how much money you will make in July will be:

`y=3^x`

The first option is correct.