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

Question

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.