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Exponential vs. Linear Models

Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
Exponential vs. Linear Models
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787 KB|16 pages
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Students will compare linear and exponential models and solve problems, observe using tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, and write a function that describes a relationship between two quantities.

Included in this Unit:
1. Task #1: students have to decide if given the opportunity to receive $1000 a day for 30 days or a penny on the first day, two pennies on the second day, and so on for 30 days, what would they choose? Students can do the calculations themselves individually or with a partner. I like to ask the class to raise their hands and see how many would pick the penny and how many the $1000. Then I ask the students after the tenth day how much those who chose the $1000 a day have in total so far ($10,000) and how much those who chose the penny have in total ($10.23). At this point those who chose the $1000 are super happy about their choice. Then I do the same thing after 20 days. By now those who chose the $1000 option have a total of $20,000 while those who chose the penny have a total of $10,485.75. Still, those who chose the $1000 are happy. But then once the students finish all three days, they can’t believe how much money those who chose the penny have. This is a great introduction to discussing or reviewing exponential growth versus linear growth.
2. Task #2: Given a set of data, students are to determine whether it can be modeled by a linear function or an exponential function. I like to do this task whole class as a guided practice. I let them try to figure it out on their own and talk it out as a class, but I guide their reasoning and answers.
3. Task #3: Students are given two sets of data to analyze and determine whether it can be modeled as a linear function or exponential function. Then the third problem brings them back to task #1 where they have to establish a connection on how the first choice of $1000 a day represents a linear model while the penny a day that doubles represents an exponential model.
4. Task #4: this is a short review on linear equations, but it covers a lot! Students practice finding slope, writing equations given a point and the slope in point-slope form, slope-intercept form, and standard form. They also practice writing equations of lines that are parallel and perpendicular to another line.
5. Task #5: This is a fun puzzle where students have to unscramble the words and then use selected letters to come up with a phrase.

Total Pages
16 pages
Answer Key
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Teaching Duration
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