Determining the monthly cost growth while taking the initial start-up price into account in order to determine the slope.

Question

Number of Months Cost ($)

1
74
2
99
3
124
4
149
The table below shows the cost for a gym membership at the local fitness center with an initial start-up fee charged in the first month. Find the slope, or monthly cost.
(1 point)
$49
• $74
$25
$37.25

Answer 1

To find the slope representing the monthly cost for the gym membership, we first need to identify the costs for each month and how they grow over time.

The costs given are:

• Month 1: $74
• Month 2: $99
• Month 3: $124
• Month 4: $149

The slope can be found by determining the increase in cost from one month to the next.

Let's calculate the difference in cost month by month:

• From Month 1 to Month 2:
  \(99 - 74 = 25\)

• From Month 2 to Month 3:
  \(124 - 99 = 25\)

• From Month 3 to Month 4:
  \(149 - 124 = 25\)

The consistent increase in the cost each month is $25.

Now, since the slope represents the monthly cost after accounting for the initial start-up fee, we conclude that the monthly cost (slope) is:

\[ \text{Monthly Cost} = \text{Slope} = 25 \]

Thus, the correct answer is $25.