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Use the table to answer the question. Determining the monthly cost growth while taking the initial start-up price into account in order to determine the slope. 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) Responses $37.25 $37.25 $25 $25 $74 $74 $49

1 answer

To determine the monthly cost (or slope) from the data provided, we can find the change in cost over the change in time (months).

Let's analyze the data:

  • After 1 month, the cost is $74.
  • After 2 months, the cost is $99.
  • After 3 months, the cost is $124.
  • After 4 months, the cost is $149.

We can calculate the monthly cost growth (slope) by looking at the change in cost between months:

  1. From month 1 to month 2: \[ \text{Change in cost} = 99 - 74 = 25 \] \[ \text{Change in months} = 2 - 1 = 1 \] Thus, the monthly cost increase (slope) is: \[ \text{slope} = \frac{25}{1} = 25 \]

  2. From month 2 to month 3: \[ \text{Change in cost} = 124 - 99 = 25 \] \[ \text{Change in months} = 3 - 2 = 1 \] The monthly cost increase (slope) remains: \[ \text{slope} = \frac{25}{1} = 25 \]

  3. From month 3 to month 4: \[ \text{Change in cost} = 149 - 124 = 25 \] \[ \text{Change in months} = 4 - 3 = 1 \] Again, the monthly cost increase (slope) is: \[ \text{slope} = \frac{25}{1} = 25 \]

Since the cost increase has been consistent at $25 for each additional month, the slope or monthly cost is $25.

Therefore, the correct response is $25.