Carla wants to buy a boat that will have the best resale value after 3 years. 1. At one boat dealer, she found a boat she likes that sells for $15,000 and depreciates at a rate of 30% per year. What will the value be after 3 years?
2. At another dealer, she found a boat that costs $12,000 and depreciates at a rate of 20% per year. What will be the value of the boat after 3 years? 3. Which boat will have the greater value in 3 years? Sep 12­10:46 AM
Rate of Change
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Key Points:
­ It is a ratio describing how one quantity changes as another quantity changes. ­Slope? ­Positive rate of change ­­> function increases over time
­Negative rate of change ­­> function decreases over time
­Linear Functions? ­ You can find the rate of change for a function on an interval
­The rate of change on an interval is the average rate of change for that period.
­ Rate of change 0? Horizontal line! ­ Vertical line? Undefined slope! Sep 12­10:53 AM
Calculating Rate of Change from a Table
1. Choose two points from the table
2. Plug them into the slope formula
3. Result is rate of change for the interval between the two points
*Note: ­For a line, the rate of change will be the same no matter what 2 points you choose.
­For an exponential function?
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Example 1
X
Y
­2
4
­1
1
0
­2
1
­5
2
­8
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Calculating Rate of Change from an Equation of a Linear Function
1. Make sure equation is in y = mx + b form. 2. Identify the slope (m) of the function.
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Example 2
2x ­ 3y = 6
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Calculating Rate of Change from an Equation of an Exponential Function
1. Look at your given interval, pick the two x­
values given to you.
2. Plug each x­value one at a time, get y, set up points.
3. Use slope formula.
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Example 3
Calculate rate of change from ­2 < x < 4 for the function: y = 2(3)x
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Example 4
Find the average rate of change on the interval:
­2 < x < 1
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Homework: Rate of Change Practice worksheet
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