I share a room with our US History teacher. I stopped by today, and caught a bit of a lesson on the Arawaks, and what Columbus and his men did to them in their search of gold. It was a fascinating lesson, and reflected the theme across the Americas from 1492 onward.

But of course I brought it back to the math. After all, students should be able to

**F-LEA.1**: Distinguish between situations that can be modeled with linear functions and with exponential functions.

**F.LEA.2**: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

**F.LEA.5**: Interpret the parameters in a linear or exponential function in terms of a context.

So I built this:

(link here)

There’s so much here. Students should play with the graph, find the rate of decay, find the entire function, and make some inferences about the population. Some questions I’d like to ask to probe for understanding:

- What is a reasonable domain and range for this function?
- What parts of the graph are reasonable? What parts are unreasonable?
- How could a piecewise function better model this situation?
- How many Arawaks do you think there were on Hispaniola in 1480?

Our US HIstory teacher said he could probably find some data on Mesoamerica. WIth this built, it’s pretty easy to plug in a new set of data and create a few new models for students to play with and analyze. I’m excited.

What am I missing? What are some other questions? Some other contexts to have students practice? Any ideas for the Desmos graph?

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howardat58Hi Dylan

My first question is “Why don’t we have more data?”

There are only 3 meaningful dots, as the third and the fourth are zero. Not a lot for estimating a best fit function.

My second question relates to the CCSS doc where I found this:

Linear, Quadratic, and Exponential Models★ F -LE

Even though there is absolutely no mention of quadratic in the following text it seems to me that you could try a quadratic in this case.

I like your question : whereabouts in the range is your graph useless? (my words!)

I would also ask “Where did this data come from and how reliable is it?”

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