Checklist and Assignment
Notes
Checklist:
Stuff
Assignment:
1. p 531 - 532 Quick Quiz
2. p 532 - 534 Exercises 17, 19, 21, 23, 25, 27, 29, 31, 33
Basic Skills: p 532 Exercises 11 - 16
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Key Words
Notes
Linear function
Rate of Change / Slope
Initial Value / y -intercept
rate of change = slope =
change in dependent variable
change in independent variable
We now use equations as a way to represent a function.
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Linear Functions
Notes
Linear functions are functions whose graphs are straight
lines.
Example: Plots of rain depth with respect to time:
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Rate of Change
Notes
The rate of change is a constant value, describing how
steep a linear graph will be.
Slope = Rate of change.
Large rates of change have steeper graphs.
Small rates of change have shallow graphs.
Rate of change can be calculated by finding the slope
between two points:
rate of change = slope =
(Math 1030)
change in dependent variable
change in independent variable
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Example 1 - Drawing a Linear Model
Notes
You hike a 3-mile trail, starting at an elevation of 8000
feet. Along the way, the trail gains elevation at a rate of
650 feet per mile.
1. What is the domain for the elevation function?
2. Draw a graph of the linear function that could represent
a model of the elevation as you hike along the trail.
3. Does the model seem realistic?
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Example 2 - A price-demand function
Notes
A store sells pineapples. Based on data for the prices
between $2 and $7, the storeowners created a model in
which a linear function is used to describe how the
number of pineapples could be sold per day (demand)
varies with price. ($2, 80 pineapples) is one point, ($5, 50
pineapples) is another point.
1. What is the rate of change?
2. What is the domain?
3. Is the model valid?
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Example 3 - Change in demand
Notes
Use the linear demand function in the last example to
predict the change in demand for pineapples if the price is
increased by $3.
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Example 4 - Rain Depth Equation
Notes
Use the plots of the rain depth functions to write an
equation that describes the rain depth at any time after
the storm has began. Find the rain depth 3 hours after
the storm began in each case.
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Example 5 - Alcohol Metabolism
Notes
Alcohol in the body is metabolized in a way that the
blood alcohol content decreases linearly. A study shows
for a group of fasting males who consume four drinks
rapidly, the BAC rose to a maximum of 0.08 g / 1000 mL
after about an hour. Three hours later, the BAC
decreases to about 0.04 g / 1000 mL.
1. Find a model that describes the elimination of alcohol
after the peak BAC is reached.
2. According to the model, what is BAC five hours after
the peak is reached?
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Example 6 - Price from Demand
Notes
Write the equation for the demand function for the
pineapples in a previous example. Then determine the
price that should result in a demand of 80 pineapples per
day.
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Notes
Notes