The rate of change in is constant in each table find the rate of change explain what the rate of change mean for the situation the table show the cost of a ski rental package for a given number of people
(4,160),(5,200),(6,240),(7,280)
To find the rate of change in the given table, we need to determine how much the cost changes for each additional person renting a ski package.
First, let's look at the change in cost for each additional person:
- From 4 people to 5 people, the cost increases from $160 to $200, which is an increase of $40.
- From 5 people to 6 people, the cost increases from $200 to $240, which is an increase of $40.
- From 6 people to 7 people, the cost increases from $240 to $280, which is again an increase of $40.
As we can see, the cost of the ski rental package increases by $40 for each additional person. This means that the rate of change in the table is $40 per person.
In this particular situation, the rate of change represents the additional cost incurred for each additional person renting a ski package. For instance, if a group of 5 people rents a ski package, they would have to pay $200 according to the table. If they decide to add one more person to the group, making it a group of 6 people, the cost would increase by $40 to a total of $240.
Therefore, the rate of change is essential in determining how the cost of the ski rental package is affected by the number of people in a group.
To find the rate of change in this situation, we can consider the change in cost for each additional person in the ski rental package.
Looking at the given table, we can see that as the number of people increases by 1, the cost increases by $40.
Let's calculate the rate of change:
- From (4,160) to (5,200): The change in the number of people is 5 - 4 = 1, and the change in cost is $200 - $160 = $40.
- From (5,200) to (6,240): The change in the number of people is 6 - 5 = 1, and the change in cost is $240 - $200 = $40.
- From (6,240) to (7,280): The change in the number of people is 7 - 6 = 1, and the change in cost is $280 - $240 = $40.
As we can see, in each case, the rate of change in the cost is $40 for each additional person.
The rate of change in this situation represents how much the cost of the ski rental package increases for each additional person. In this case, the rate of change of $40 means that for every extra person added to the package, the cost increases by $40.
To find the rate of change in a table, you can calculate the difference in the dependent variable (in this case, the cost of the ski rental package) divided by the difference in the independent variable (in this case, the number of people). Let's calculate the rate of change step by step:
1. Calculate the difference in the cost of the ski rental package:
- From (4,160) to (5,200): 200 - 160 = 40
- From (5,200) to (6,240): 240 - 200 = 40
- From (6,240) to (7,280): 280 - 240 = 40
2. Calculate the difference in the number of people:
- From 4 to 5: 5 - 4 = 1
- From 5 to 6: 6 - 5 = 1
- From 6 to 7: 7 - 6 = 1
3. Divide the difference in the cost by the difference in the number of people to find the rate of change:
- For each calculation, the difference in the cost was 40, and the difference in the number of people was 1. Therefore, the rate of change is 40/1 = 40.
Now, let's explain what the rate of change means for the situation. In this case, the rate of change of 40 means that for each additional person in the group, the cost of the ski rental package increases by $40. It indicates the constant increase in the cost per person as the number of people in the group increases.