This mathematical modeling activity from Michael Fenton begins with students looking at a familiar image and writing down what they notice and what they wonder.

From there they consider what information they need to figure out how long it will take an iPhone to charge. Students then look for patterns in the additional information provided . The activity gives students the opportunity to (1) define, evaluate, and compare functions (2) use functions to model relationships between quantities, and (3) investigate patterns of association in bivariate data. Fenton provides lesson notes, handouts, extensions, optional Desmos graphs.

This is a good problem for teachers who are working on Unit 3 in the CUNY HSE Math Curriculum Framework with their students.

In addition to being a good problem to look at rate of change and starting amount in a familiar context, this is another (optional) layer to this problem. It turns out that the relationship between the charge and the time charging is not entirely linear. The rate stays the same for the most part and then it slows down towards the end. Fenton offers an interesting way to talk about the limitation of mathematical models.