Question

Martha works at a small jewelry store. She designs 2 rings in the first hour. Every additional hour, she designs 3 new rings.

Select all the functions that can be used to find the number of rings, r(n), she designs in n hours.

Answer 1

To find the function that describes the number of rings, \( r(n) \), that Martha designs in \( n \) hours, we can analyze her design pattern:

1. In the **first hour**, she designs **2 rings**.
2. In **every subsequent hour**, she designs **3 additional rings**.

Let's break down her total production over \( n \) hours:

- For the **first hour**, she has \( 2 \) rings.
- For the remaining \( n-1 \) hours, she designs \( 3(n - 1) \) rings.

Putting this together, the total number of rings she designs in \( n \) hours can be expressed as:

\[
r(n) = 2 + 3(n - 1)
\]

Now we can simplify this equation:

\[
r(n) = 2 + 3n - 3
\]
\[
r(n) = 3n - 1
\]

Thus, the function that represents the number of rings Martha designs in \( n \) hours is:

\[
r(n) = 3n - 1
\]

### Conclusion:
The function that can be used to find the number of rings Martha designs in \( n \) hours is:

- \( r(n) = 3n - 1 \)

If you have other functions or options to consider, please provide them for evaluation.