Represent a story context as a geometric sequence using tables, graphs, and equations.
Identify the constant growth factor in each of the representations.
Use function notation to write the recursive equation for a geometric sequence
Today's Materials:
Laptop
Pencil
Guided Note Sheet
Please complete the Jump Start (activator). You have 5 minutes before we review. This is independent it should be silent.
Jump Start - 5 minute
Required
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Question 1
1.
In 2-3 sentences respond to the following:
Have you ever seen a message, as displayed in the image, in a text, email, social media, etc.? How quickly do you think this message would spread if everyone participated in sharing the message?
Super Scooper Ice Cream Chain Email
Hi! My name is Bill Weights, founder of Super Scooper Ice Cream. I am offering you a gift certificate for our signature "Super Sundae" (an $11.95 value) if you forward this letter to 10 people.
When you have finished sending this letter to 10 people, a screen will come up. It will be your Super Sundae gift certificate. Print that screen out and bring it to your local Super Scooper Ice Cream store. The server will bring you the most wonderful ice cream creation in the world—a Super Sundae with three yummy ice cream flavors and three toppings!
This is a sales promotion to get our name out to young people around the country. We believe this project can be a success, but only with your help. Thank you for your support.
Sincerely,
Bill Weights, Founder of Super Scooper Ice Cream
These chain emails rely on each person who receives the email to forward it on. Have you ever wondered how many people might receive the email if the chain remains unbroken? To figure this out, assume that it takes a day for the email to be opened, forwarded, and then received by the next person. On day 1, Bill Weights starts by sending the email out to his 8 closest friends. They each forward it to 10 people so that on day 2 it is received by 80 people. The chain continues unbroken.
1st Read:
Read so you can tell the story. Don’t worry so much about the mathematical details, just understanding the main details of the email.
2nd Read:
Read for the mathematics. What do we know? What do we want to know?
3rd read:
One last read, to think about the strategy you'd use to find the amount of people who would have recieved the email if the pattern continued.
(Think about table, graph, equations, diagrams)
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Question 2
2.
How many people will receive the email by day 5?
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Question 3
3.
How many people will recieve the email on day 7?
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Question 4
4.
How many people will recieve the email on day n? Explain your answer with as many representations as needed.
Guided Notes Paper:
Lets do some guided notes on the provided paper.
Table (numerical)
Graph (Graphical)
Recursive
Explicit Equation
Let's try this together...
Reminder:
Identify a first term
Determine the common ratio.
Use the appropriate structure to write the recursive equation.
Use the appropriate structure to write the explicit equation. (Remember you can write a equivalent equation for n=0 or n=1)
Required
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Question 5
5.
Write the recursive equation.
Required
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Question 6
6.
Write the explicit equation.
Independently try this...
Reminder:
Identify a first term
Determine the common ratio.
Use the appropriate structure to write the recursive equation.
Use the appropriate structure to write the explicit equation. (Remember you can write an equivalent equation for n=0 or n=1)
Required
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Question 7
7.
Independently try this.
Write the recursive equation.
Required
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Question 8
8.
Write the explicit equation.
Practice/Intervention
In the next problems, you are given various types of information. Write the recursive and explicit functions for each geometric sequence.
Required
1 point
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Question 9
9.
2, 4, 8,16,...
Write the recursive equation.
Required
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Question 10
10.
2, 4, 8,16,...
Write the explicit equation.
Required
1 point
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Question 11
11.
Claire has $300 in an account. She decides she is going to take out half of what’s left in there at the end of each month.
(Hint: Think about if this starts at month 0 or month 1?)
Write the recursive equation.
Required
1 point
1
Question 12
12.
Claire has $300 in an account. She decides she is going to take out half of what’s left in there at the end of each month.
(Hint: Think about if this starts at month 0 or month 1?)
Write the explicit equation.
Required
1 point
1
Question 13
13.
Write the recursive equation.
Required
1 point
1
Question 14
14.
Write the explicit equation.
Required
1 point
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Question 15
15.
Write a recursive equation.
The first term in this geometric sequence is 125. The next term is 25 and every term after that is found by dividing by 5.
Required
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Question 16
16.
Write a explicit equation.
The first term in this geometric sequence is 125. The next term is 25 and every term after that is found by dividing by 5.
