Compare decreasing arithmetic and geometric sequences.
Understand that if a geometric sequence has a common ratio of 0<r<1, the sequence is decreasing.
Understand that if an arithmetic sequence has a negative common difference, the sequence is decreasing.
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.
Required
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Question 1
1.
Jump Start:
The Super Discount store is having a sale and all the clearance items are 40% off.
Which of the following are correct to find the price of an item that is normally $25.00 @ 40% off?
Required
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Question 2
2.
What is the price of the item after the discount?
Launch!
Today we will discuss and analyze data based on a real world issue, animal population decrease.
Explore and Discuss
Let's look at an example of this in relation to our work so far this unit.
In 1884, Springfield residents Orick Greenleaf and Everett Barney donated 243 acres of land for the creation of an urban park to be named Forest Park. Through donations of land over time it grew to 735-acres including the Forest Park Zoo, ducks ponds, a rose garden, an indoor skating rink, hiking trails, ball fields, basketball courts, a swimming pool, a picnic area, tennis courts, and much more.
Starting in the mid 1950's, acres of land in Forest Park once filled with forest were sold and used to construct landmarks, the Springfield and Longmeadow surrounding neighborhoods , and Interstate 91.
As the land had become more desired and valuable for humans, the size of the park has been reduced over time. The following data has been collected about this reduction:
The data table below shows the amount of acres over a five-year span in one of the sections of Forest Park:
Use n to represent the number of years"
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Question 3
3.
Write the recursive equationthat models the acres in this section.
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Question 4
4.
Write the explicit equationthat models the acres in this section.
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Question 5
5.
What type of sequence does the acres data represent?
The data for amount of acres left was stopped when it was at 76.5 acres. Biologists who studied the animal wildlife found in that area seen the population was declining at the alarming rate of 20% per year. They determined that the decline was due to several factors, including the reduction of habitat from selling off the land. When they began taking data, the animal population in the sold area was about 600 individuals. The data for the population is shown below:
Use n to represent the number of years"
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Question 6
6.
Write the recursive equation that models the population data.
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Question 7
7.
a. Write the explicit equation that models the population data.
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Question 8
8.
What type of sequence does the acres data represent?
Sequence Reminders:
Arithmetic Sequences
Common Difference (d)
Straight lines
Recursive
Explicit
Geometric Sequences
Common Ratio (r)
Curved Lines
Recursive
Explicit
Quick Group Presentation !🙌
Your group will be responsible to present the similarites and differences between the equations, graphs, etc. shown on your card to the class.
You have 3 minutes to present your infomation so be ready and precise.
Independent Quiz Lesson 1-4
You may use all of your notes.
Lesson Closure:
How are decreasing arithmetic sequences different from decreasing geometric sequences?
