The table below gives a cost per person to rent a fishing charter but find the rate of change given that it is constant. Also explain what the rate of change means for the situation people 2345 cost 110, 165 to 220,275
To find the rate of change, we can use the formula: Rate of change = (Change in cost)/(Change in number of people).
Let's calculate the changes:
- Change in cost = Final cost - Initial cost = 165 - 110 = 55
- Change in number of people = Final number of people - Initial number of people = 275 - 2345 = -2070
To find the rate of change, we divide the change in cost by the change in number of people:
Rate of change = 55/(-2070) = -0.026570048309178744
The rate of change is approximately -0.0266.
For this situation, the negative rate of change means that as the number of people increases, the cost per person decreases. In other words, the more people there are, the cheaper it becomes per person to rent the fishing charter.
To find the rate of change, we can calculate the difference in cost per person between two consecutive data points and divide it by the corresponding difference in the number of people.
First, let's calculate the rate of change between the first two data points:
Rate of change = (Cost difference) / (People difference)
Rate of change = (165 - 110) / (1650 - 1100)
Rate of change = 55 / 550
Rate of change = 0.10
Next, let's calculate the rate of change between the second and third data points:
Rate of change = (Cost difference) / (People difference)
Rate of change = (275 - 220) / (2345 - 1650)
Rate of change = 55 / 695
Rate of change ≈ 0.08
The rate of change measures how much the cost per person changes for each additional person. In this case, the rate of change is constant, meaning that the cost per person increases by a fixed amount for each additional person.
For example, with the first rate of change of 0.10, the cost per person increases by $0.10 for each additional person. So, if there are 2,345 people, the cost per person is $110, for 2,350 people it would be $110.10, for 2,355 people it would be $110.20, and so on.
Similarly, with the second rate of change of 0.08, the cost per person increases by $0.08 for each additional person.