IM Alg2.1.9 Lesson: What’s the Equation?
[size=150]For the function [math]f(x)=32\cdot(\frac{3}{4})^x[/math], evaluate mentally:[br][/size][math]f(0)[/math]
[math]f(1)[/math]
[math]f(2)[/math]
[math]f(3)[/math]
A large cake is in a room.
[size=150]The first person who comes in takes [math]\frac{1}{3}[/math] of the cake. Then a second person takes [math]\frac{1}{3}[/math] of what is left. Then a third person takes [math]\frac{1}{3}[/math] of what is left. And so on.[/size]
Complete the table for C(n), the fraction of the original cake left after n people take some.
Write two definitions for [math]C[/math]: one recursive and one non-recursive.[br]
What is a reasonable domain for this function? Be prepared to explain your reasoning.[br]
On graph paper, draw a square of side length 1.
[size=150]Draw another square of side length 1 that shares a side with the first square. Next, add a 2-by-2 square, with one side along the sides of [i]both[/i] of the first two squares. Next, add a square with one side that goes along the sides of the previous two squares you created. Next, do it again.[br]Pause here for your teacher to check your work.[/size]
Write a sequence that lists the side lengths of the squares you drew.[br]
Predict the next two terms in the sequence and draw the corresponding squares to check your predictions.[br]
Describe how each square’s side length depends on previous side lengths.[br]
Let [math]F(n)[/math] be the side length of the [math]n^{th}[/math] square. So [math]F(1)=1[/math] and [math]F(2)=1[/math]. Write a recursive definition for [math]F[/math].[br]
Is the Fibonacci sequence arithmetic, geometric, or neither? Explain how you know.
[size=150]Look at quotients [math]\frac{F(1)}{F(0)},\frac{F(2)}{F(1)},\frac{F(3)}{F(2)},\frac{F(4)}{F(3)},\frac{F(5)}{F(4)}[/math]. [/size][br]What do you notice about this sequence of numbers?
The 15th through 19th Fibonacci numbers are 610, 987, 1597, 2584, 4181. [br]What do you notice about the quotients[math]\frac{F(16)}{F(15)},\frac{F(17)}{F(16)},\frac{F(18)}{F(17)},\frac{F(19)}{F(18)}[/math]?[br]
IM Alg2.1.9 Practice: What’s the Equation?
A party will have hexagonal tables placed together with space for one person on each open side:
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[/img]
Complete this table showing the number of people P(n) who can sit at n tables.
Describe how the number of people who can sit at the tables changes with each step.[br]
Explain why [math]P(3.2)[/math] does not make sense in this scenario.[br]
Define [math]P[/math] recursively and for the [math]n^{th}[/math] term.[br]
Diego is making a stack of pennies. He starts with 5 and then adds them 1 at at time. A penny is 1.52 mm thick. Complete the table with the height of the stack h(n), in mm, after n pennies have been added.
Does [math]h(1.52)[/math] make sense? Explain how you know.[br]
A piece of paper has an area of 80 square inches.
[size=150]A person cuts off [math]\frac{1}{4}[/math] of the piece of paper. Then a second person cuts off [math]\frac{1}{4}[/math] of the remaining paper. A third person cuts off [math]\frac{1}{4}[/math] what is left, and so on.[/size]
Complete the table where A(n) is the area, in square inches, of the remaining paper after the n^th person cuts off their fraction.
Define [math]A[/math] for the [math]n^{th}[/math] term.[br]
What is a reasonable domain for the function [math]A[/math]? Explain how you know.[br]
Here is the recursive definition of a sequence:
[math]f(1)=35,f(n)=f(n-1)-8[/math] for [math]n\ge2[/math].[br][br]List the first 5 terms of the sequence.[br]
Graph the value of each term as a function of the term number.
Here is a graph of sequence q.
[img]data:image/png;base64,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[/img][br]Define [math]q[/math] recursively using function notation.
Here is a recursive definition for a sequence f:
[math]f(0)=19,f(n)=f(n-1)-6[/math][size=150] for [math]n\ge1[/math].[br] The definition for the [math]n^{th}[/math] term is [math]f(n)=19-6\cdot n[/math] for [math]n\ge0[/math].[/size][br][br]Explain how you know that these definitions represent the same sequence.[br]
Select a definition to calculate [math]f(20)[/math], and explain why you chose it.[br]
An arithmetic sequence j starts 20, 16, . . .
Explain how you would calculate the value of the 500th term.