Surface the difference between a discrete and continuous model for a given context.
Introduce continuous exponential functions.
Recognize that arithmetic sequences are linear functions by examining the constant rate of change.
Recognize that geometric sequences are exponential functions by examining the constant ratio of values over equal intervals.
Introduce the concept of the domain of a function defining the possible input values.
Today's Materials:
Laptop
Pencil
Guided Note Sheet
Binder
Please complete theJump Start (activator). This is independent it should be silent.
Question 1
1.
Describe what a discrete function would look like on a graph.
Question 2
2.
Describe what a continuous function would look like on a graph.
Launch, Explore, Discuss
We are beginning on the guided notes paper. Problems 1-4.
Launch, Explore, Discuss
Lets compare the problem 1-4 to find similarities and differences with each other.
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Question 3
3.
Compare problems 1 and 2. What similarities do you see? What differences do you notice?
Similarites:
Both functions are __________
Both functions have a __________ rate of change.
Differences:
Problem #1 is __________
Problem #2 is __________
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Question 4
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Question 5
5.
Lesson Summary:
In this lesson, we learned that the possible inputs for a function are called the domain. We found that some situations are best described using a discrete model and others are represented better with a continuous model. Arithmetic sequences are part of the linear family of functions and geometric sequences are part of the exponential family of functions.
Question 6
6.
Closure - Debreif: What is the mathematical reason that the dots are connected on some graphs and not on others?
Independent Practice
Instructions:
Predict the next two terms in the sequence. State whether the sequence is arithmetic, geometric, or neither.
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Question 7
7.
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Independent Practice
Instructions:
Identify whether the following statements represent a discrete or a continuous relationship.
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Question 12
12.
The hair on your head grows 1/2 inch per month
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Compare problems 1 and 3. What similarities do you see? What differences do you notice?
Similarites:
Both functions are __________
Both functions are __________
Differences:
Problem #1 is __________
Problem #3 is __________
Compare problems 3 and 4. What similarities do you see? What differences do you notice?
Similarites:
Both functions have a __________ ratio between outputs.
Differences:
Problem #3 is __________
Problem #4 is __________
Problem #3 is__________
Problem #4 is __________
Predict the next two terms in the sequence.
Question 8
8.
State whether the sequence is arithmetic, geometric, or neither.
Question 9
9.
State whether the sequence is arithmetic, geometric, or neither.
Question 10
10.
Predict the next two terms in the sequence.
Question 11
11.
State whether the sequence is arithmetic, geometric, or neither.
Discrete
Question 13
13.
The city of Buenos Aires adds 6,000 tons of trash to its landfills every day.
Independent Practice
Instructions:
Show your work!
Question 14
14.
Apples are on sale at the market at 4 pounds for $2.00. What is the price for 1 pound?
Question 15
15.
One dozen (12) eggs cost $1.98. How much does 1 egg cost? (Round to the nearest cent.)
Question 16
16.
Best Shoes had a back to school special. The total bill for 4 pairs of shoes came to $69.24 (before tax). What was the average price for each pair of shoes?
