Question

Using the table below, create a function that represents the cost of a monthly museum membership.



This question is worth 3 points. Be sure to show your work.

1. Describe the initial value

2. Describe the rate of change

3. Provide the function in the form y = mx + b

Answer 1

To create a function that represents the cost of a monthly museum membership, we first need to analyze the provided table (which, for the sake of this exercise, I'll create an example table based on common membership tiers).

### Example Table of Monthly Museum Membership Costs:

| Month | Cost ($) |
|-------|----------|
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
| 5 | 50 |
| 6 | 60 |

### 1. Describe the initial value:
The initial value refers to the cost of the membership at the starting point (Month 1). From our example table, the cost for Month 1 is **$10**. This represents the cost when the number of months is zero, essentially the starting fee from which subsequent costs are derived.

### 2. Describe the rate of change:
The rate of change indicates how much the cost increases with each additional month. In our table, we observe that the cost increases by **$10** for each additional month. Thus, the rate of change (slope) is **10** dollars per month.

### 3. Provide the function in the form y = mx + b:
In the context of a linear function where:
- \( y \) represents the total cost,
- \( m \) is the rate of change,
- \( x \) is the number of months, and
- \( b \) is the initial value.

Given:
- \( m = 10 \) (the cost increases by $10 each month),
- \( b = 0 \) (assuming the initial cost for 0 months is $0; if you want to include the cost for those who already have a membership, it starts from $10, so \( b \) can be considered as the constant fee).

The function can be expressed as:

\[
y = 10x + 0
\]

If starting from Month 1, to consider initialization:
\[
y = 10x + 0 \quad \text{(for x = number of months)}
\]

Thus, the final function representing the cost of a monthly museum membership is:

\[
y = 10x
\]

Where \( y \) represents the total cost for \( x \) months.