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Question 219411: How do you find the rate of change?
The cost of group musuem tickets is $48 for four people and $78 for ten people.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you find the rate of change?
The cost of group musuem tickets is $48 for four people and $78 for ten people.
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You have two points: (4,48) and (10,78).
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rate of change = slope = (78-48)/(10-4) = 30/6 = $5 for each additional person.
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Cheers,
Stan H.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! You start off with $48 for 4 people.
You end up with $78 for 10 people.
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The cost per person for 4 people was $48/4 = $12 per person.
The cost per person for 10 people was $78/10 = $7.8 per person.
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The cost per person is going down.
At what rate?
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If you take a straight line average, then you would find the average rate of change by dividing the difference in cost per person by the difference in the number of people and you would say that's your rate of change in the cost per person.
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Let's see how that works.
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Change in cost per person went from $12.00 to $7.8
that's a difference of $4.20
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Change in number of people went from 4 to 10
That's a difference of 6
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The average rate of change in the cost per person was $-4.20 / 6 = -$.70 per person.
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If you have 4 people, the cost is $12.00
If you have 5 people, the cost is $11.30
If you have 6 people, the cost is $10.60
If you have 7 people, the cost is $9.90
If you have 8 people, the cost is $9.20
If you have 9 people, the cost is $8.50
If you have 10 people, the cost if $7.80
etc.
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The cost per person is going down by $.70 per additional person.
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The equation to express this would be:
y = 12 - .70*(x-4)
The graph of that would be:
The horizontal lines at 12 and 8 are just there to show you the values when x = 4 and when x = 10.
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The equation to tell you what the total cost would be can be derived from this.
that equation would be:
y = x*(12 - .70*(x-4))
The graph of that would be:
The horizontal lines at 48 and 78 are just there to show you the values when x = 4 and when x = 10.
While the rate of change in the cost per person was linear (previous graph), the rate of change in the total cost is not.
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In general, the rate of change is the change in the value of the dependent variable divided by the change in the value of the independent variable.
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y is usually the dependent variable.
x is usually the independent variable.
this translates to a change in the value of y divided by a change in the value of x per unit of x.
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We tracked cost per person and identified the rate of change in the cost per person as the number of people changed.
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