Question

The cost of purchasing an all-day lift ticket at Greek Peak Ski Resort for various numbers of days are shown in the table below: number of days cost 1 $82 2 $156 3 $226 4 $295 5 $362. (a) Approximate the slope of this linear model. (b) Explain your estimation strategy for part (a). (c) What is the meaning of this slope in this situation? Use quantitative values here as you say what the slope means in the context of the ski resort pricing (including units).

Answer 1

To approximate the slope of the linear model, we can use the formula: slope = (change in cost) / (change in number of days). The approximate slope of this linear model is $70. This means that for each additional day, the cost of the all-day lift ticket increases by $70.

Step-by-step explanation:

To approximate the slope of the linear model, we can use the formula:

slope = (change in cost) / (change in number of days)

Using the given values, we can calculate the changes in cost and number of days for different scenarios:

For 1 day to 2 days: change in cost = $156 - $82 = $74, change in number of days = 2 - 1 = 1

For 2 days to 3 days: change in cost = $226 - $156 = $70, change in number of days = 3 - 2 = 1

For 3 days to 4 days: change in cost = $295 - $226 = $69, change in number of days = 4 - 3 = 1

For 4 days to 5 days: change in cost = $362 - $295 = $67, change in number of days = 5 - 4 = 1

Calculating the average change in cost and number of days:

Average change in cost = ($74 + $70 + $69 + $67) / 4 = $70

Average change in number of days = 1

Therefore, the approximate slope of this linear model is $70. This means that for each additional day, the cost of the all-day lift ticket increases by $70.