Believe it or not you can cook chestnuts in a microwave oven. And they taste pretty good provided you get the cooking time just right. Microwaves are powerful, so there’s little room for error. A few seconds too few and they’re virtually raw, a few seconds too many and they’re rubbery or hard. They don’t caramelize as well as roasted chestnuts but they do caramelize somewhat, and they retain a lot more moisture. The table below shows the cook times I arrived at through trial and error for chestnuts in batches of two, three, four, and five. These results were derived by using medium-to-large fresh chestnuts in a 1000-watt oven that has a turntable. I also carved an “X” into at least one side of each chestnut with a sharp knife prior to cooking.

The freshness matters a lot because freshness equates to moisture content, and moisture content dictates cook times. Fresh ones are brightly colored and fill their shells. Anything that gives a lot when you squeeze it and has a uniform, dark brown color has already dried out. Cook it in a microwave and it’ll come out rock hard.

**Now to the Algebra part.** Suppose you wanted to use the data above to create a “recipe” for microwaving chestnuts – a formula that you or someone else could use for cooking batches of six, seven, eight chestnuts or more (theoretically).

Think of the left column as your x-values and the right column as your y-values. Notice how for each additional chestnut the number of seconds added increases each time, it’s not constant. So we know this would not be a linear function. Let’s assume that it is an exponential function – that it follows the form y = abˣ. How could you use this data to create an exponential function, and what would the resulting “recipe” be?