Video Check: Select all that apply with regards to the video embedded directly above this item.
Embedded below is an online Tower of Hanoi puzzle that you may find helpful.
10 points
10
Question 2
2.
Solve It! You are to move the stack of 5 rings to another post.
Here are the rules:
◆ A move must consist of taking the top ring from one post and placing it onto another post.
◆ You can move only one ring at a time.
◆ Do not place a ring on top of a smaller ring.
Consider the fewest number of moves needed to solve pyramids composed of 1, 2, 3... rings. Match the correct minimum number of moves on the left with each pyramid described on the right.
Hint: Consider modeling the scenario with an equation in the following format:
where m = number of moves, n = number of rings, and a is a constant.
1 move
2 moves
3 moves
5 moves
10 moves
31 moves
42 moves
1023 moves
1,048,575 moves
2,531,703 moves
Pyramid with 1 ring
Pyramid with 2 rings
Pyramid with 5 rings
Pyramid with 10 rings
Pyramid with 20 rings
3 points
3
Question 3
3.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 4
4.
Take Note: What is the general form of an exponential function? Enter only the equation.
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10
Question 5
5.
Take Note: In the general form of an exponential function, y=ab^x, which parameter or variable represents the base, which is a constant greater than 0 and not equal to 1?
10 points
10
Question 6
6.
Take Note: In the general form of an exponential function, y=ab^x, which parameter or variable is multiplied by the base and cannot equal 0?
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10
Question 7
7.
Take Note: In the general form of an exponential function, y=ab^x, which parameter or variable represents the independent variable?
10 points
10
Question 8
8.
Take Note: What is the domain of ALL exponential functions?
30 points
30
Question 9
9.
Problem 1 Got It? Graph the functions in the same coordinate plane using contrasting colors. Include all relevant graph detail and label the functions.
Graph the functions by hand first, but you may check your graphs with Desmos and make edits as needed.
You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.
10 points
10
Question 10
10.
Problem 1 Got It? Reasoning: What generalization(s) can you make about the domain, range, and y-intercepts of these functions? Select all that apply.
3 points
3
Question 11
11.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 12
12.
Take Note: Consider the general form of an exponential function.
y=ab^x
If the function represents exponential growth, what do you know about a and b ?
Select all that apply.
10 points
10
Question 13
13.
Take Note: Consider the general form of an exponential function.
y=ab^x
If the function represents exponential decay, what do you know about a and b ?
Select all that apply.
10 points
10
Question 14
14.
Take Note: Graph an example of an exponential growth function. Zoom and pan your graph to establish an appropriate viewing window.
Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
10 points
10
Question 15
15.
Take Note: Graph an example of an exponential decay function. Zoom and pan your graph to establish an appropriate viewing window.
Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
10 points
10
Question 16
16.
Take Note: What is an asymptote ?
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10
Question 17
17.
Take Note: Sketch the graph of an exponential growth function with a horizontal asymptote at y=2.
10 points
10
Question 18
18.
Take Note: What is the range of ALL exponential growth and exponential decay functions?
10 points
10
Question 19
19.
Problem 2 Got It?
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10
Question 20
20.
Problem 2 Got It?
10 points
10
Question 21
21.
Problem 2 Got It? You put $2000 into a college savings account for four years. The account pays 6% interest annually. Is this situation an example of exponential growth or decay? What is the y-intercept?
3 points
3
Question 22
22.
Video Check: Select all that apply with regards to the video embedded directly above this item.
20 points
20
Question 23
23.
Take Note: Consider the general form of an exponential function. y=ab^x
Categorize each of the items on the left as representing either exponential growth or exponential decay.
b = 1 + r (r is a positive quantity)
r is the percent decrease, written as a decimal & is called the rate of decay or decay rate
b is the decay factor
b = 1 + r (r is a negative quantity)
r is the percent increase, written as a decimal & is called the rate of increase or growth rate
b is the growth factor
y increases by a constant percentage each time period
b > 1
y decreases by a constant percentage each time period
0 < b < 1
Exponential growth
Exponential decay
Consider the exponential growth & decay model.
10 points
10
Question 24
24.
Take Note:
What does A(t) represent?
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10
Question 25
25.
Take Note:
What does t represent?
10 points
10
Question 26
26.
Take Note:
What does a represent?
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10
Question 27
27.
Take Note:
What does r represent?
10 points
10
Question 28
28.
Problem 3 Got It? Suppose you invest $500 in a savings account that pays 3.5% annual interest. How much will be in the account after five years?
3 points
3
Question 29
29.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 30
30.
Take Note: Summarize the process of using exponential growth and a table that was demonstrated in Problem 4.
10 points
10
Question 31
31.
Problem 4 Got It? Suppose you invest $500 in a savings account that pays 3.5% annual interest. When will the account contain at least $650?
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10
Question 32
32.
Problem 4 Got It?Reasoning: Use the table in Problem 4 (provided again below) to determine when that account will contain at least $1650. Explain.
3 points
3
Question 33
33.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 34
34.
Take Note: What is the difference between discrete functions and continuous functions?
10 points
10
Question 35
35.
Take Note: Sketch a discrete function using orange and a continuous function using blue.
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10
Question 36
36.
Take Note: How can you determine the growth factor or decay factor from discrete data?
10 points
10
Question 37
37.
Problem 5 Got It? For the model in Problem 5, what will the world population of liberian lynx in 2020?
10 points
10
Question 38
38.
Problem 5 Got It?Reasoning: If you graphed the model in Problem 5, would it ever cross the x-axis? Explain.
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10
Question 39
39.
🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?
