One strategy that I often use is to have students gather data and then find a regression equation. I’ve done this with both linear and radical functions. Next up: exponential functions in this exponential decay activity.
In order for students to really understand what the a-value and b-value represent in the equation y=ab^x, I give them this assignment. Each pair of students gets a checkerboard with a different pattern. Some are true checkerboards, but some have more or less black squares than usual.
The Exponential Activity
Once they have a checkerboard, the students get a small cup of beans (or M&M’s if I’m feeling nice 😏) to spill onto the checkerboard. Remove any beans that land on a black square from the pile. Repeat the process for the remaining beans. The number of beans remaining is recorded after each round, which gives students….*ta da* a set of exponential data!
Here is where a graphing calculator or Desmos.com come into play. First, have the students look at their plotted data…it’s VERY exponential. Therefore, it’s worth discussing why the data is exponential and not linear. The student worksheet asks them about this.
Next students calculate the regression model for their data, which gives them the a-value and a b-value of the exponential model. Alternatively, you could have students build their own exponential model since they know the starting number of beans and the decay rate.
The Takeaway
Finally, graph the regression equation along with the scatterplot of the points. TELL me your students aren’t amazed at how well the equation fits the data. Now the students analyze their equation. Students tell what their a- and b-values represent and how to determine them without a calculator. LOTS of great discussion comes about from this activity, and students develop a true understanding of the components of an exponential equation.
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Happy teaching!
Natasha