# Kate Nowak’s epic Credit Cards/Exponential Functions Unit

This packet really builds up to and where that number comes from. It’s designed for 3 days.

Here tis.

# Dan Meyer’s Three-Act Problems and Exponential Functions

There’s two good ones that I know of. Maybe there are more:

I think that these will show up when I’m doing Geometric Sequences, before we prove a bunch of stuff about exponents and powers.

# Negative bases and exponential functions

Graph .

I’d like to do this problem after we know about rational functions. We’ll start with integer inputs and then move to rational inputs, where we quickly run into the sort of domain problem we have with radicals and negatives.

Maybe even better: let’s play with this function again once we know about complex numbers and try to graph this function again. There’s another host of problems waiting for us there, even conceived as a real –> complex function.

[See also: http://mathforum.org/library/drmath/view/55604.html]

# Irrational numbers raised to irrational powers

# Bouncing balls and line of best fit

“A basketball is dropped from different heights, and the height of the first bounce is measured each time. What is the relationship between the height of the drop and the height of the bounce?”

Click me! NOW.

# Dice and linear regression

OK, now here’s a regression problem that I can get behind. Via CME:

“Roll 1 die. Write down what you roll. Roll 2 dice. Write down the sum of all the numbers that you roll. Roll 3 dice. You know what to do. Roll 4. Write down the sum.”

“Predict: how much will you roll with 5 dice? 10 dice? 123 dice?”

A variant:

“Roll 1 die 3 times. How many 6’s do you roll? Roll 2, three times. How many 6’s do you roll? Continue onwards and upwards.”

Do I have to mention the connection to probability?