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. Too few seconds 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. Chestnuts were stored at room temperature.

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?