The table below gives the cost per person to buy tickets to an upcoming concert. Find the rate of change.
People Cost ($)
2
148
3 222
4 296
5 370
Responses
1481
148 over 1
174
1 over 74
741
74 over 1
1222
To find the rate of change in the cost per person for tickets to the concert, we need to calculate the change in cost over the change in the number of people. This is essentially finding the slope of the line that would connect these points if they were plotted on a graph.
Let's calculate the rate of change using the data for 3 and 4 people, which have clear cost values provided.
For 3 people, the cost is $222.
For 4 people, the cost is $296.
Now, calculate the change in cost and the change in the number of people:
Change in cost (ΔCost) = Cost for 4 people - Cost for 3 people
ΔCost = $296 - $222
ΔCost = $74
Change in the number of people (ΔPeople) = 4 people - 3 people
ΔPeople = 1
Now we find the rate of change, which is ΔCost / ΔPeople:
Rate of Change = ΔCost / ΔPeople
Rate of Change = $74 / 1
Rate of Change = $74 per additional person
So the correct rate of change is 74 over 1 or $74 per person. The correct choice is:
741
74 over 1