If you used a variable in your description, explain its meaning.
c.
What is the 100th entry in the table?
d.
Is 102 ever an "output"? How do you know?
Problem H2
Mr. Lewis looked at the table in Problem H1 and said, "Oh, I get it. Just do these steps."
1.
First, you multiply the input number by itself and multiply that answer by 6.
2.
Then you add 6 to the answer you just got, and call that number A.
3.
Then, start over. Multiply the input number by itself and add 11, and call that B.
4.
Multiply the input number by 5, and call that C.
5.
Then, multiply B and C together, and divide by 6. Call that D.
6.
Finally, subtract D from A, and that's all!
If you do all this, you'll get the numbers in the table." Does Mr. Lewis get it? Does Mr. Lewis' method agree with yours for the first three outputs? For the next three? Which method is correct?
Problem H3
A frog climbs up the side of a well and slides back while resting. Every minute the frog leaps forward 5 meters (and it leaps forward precisely at the end of the minute). Then it rests for a minute. At the end of the rest, the frog slips back 3 meters. At the end of the next minute it leaps (5 meters), then a minute later it slides back (3 meters), and so on.
Here is a picture of a well 11 meters deep.
You may find it helpful to work with someone to model what's happening in the problem.
a.
Fill in the table below. Why is there only one correct way to fill in the table?
There are other ways to represent situations besides tables. Try drawing a visual image (a graph or a picture) that conveys information about the frog in the well.
c.
How long would it take the frog to get out of a well that is 30 meters deep? One that is 100 meters? One that is 103 meters?
Try to predict using a rule rather than extending a table. Close Tip
d.
The (tired) frog took 13 minutes to get out of the well. How deep could the well have been?
Is there only one answer to this question? Close Tip
Suppose our frog could climb 6 meters per minute and slid only 2 meters while resting. How long would it take to get out of a 100-meter well?
b.
Suppose our frog could climb n meters per minute, and slid only 2 meters while resting. Describe, in terms of n, how long it would take to get out of a 100-meter well.
c.
There are several numbers that contribute to the frog's predicament. There's the climbing rate (5 meters per minute in the original problem), the slippage rate (originally 3 meters per minute), and the height of the well. Figure out a rule that allows you to calculate the escape time if you are given the climbing rate, the slippage rate, and the height of the well. (Such a rule is called a function -- we'll look at functions in depth later on in the course.)
Similar reasoning to some of the Eric problems will be helpful here, but this is a true challenge. Close Tip
