Most of us only think about our phone battery when it's about to die.

But for Jonathan Juarez and his teammates at Cal Poly Humboldt, smartphone battery performance became the focus of their work during the 2026 Mathematical Contest in Modeling (MCM)®.

Over four days, the team researched what causes smartphone batteries to drain and how factors such as usage, temperature, and battery age affect performance. Their work earned them the designation of Successful Participant.

The project combined physics, mathematics, engineering, and data analysis. The team looked at how different types of phone use affect battery drain and how that changes as a battery ages. They tested their model against published data and found that it lined up closely with real-world battery behavior.

For Juarez, the experience also opened the door to research. MCM showed him that mathematical modeling could be a way to dig into questions that interested him and see where they led.

Taking Mathematics Beyond the Classroom

Like many students, Juarez was looking for a way to use what he was learning in class on something that mattered outside the classroom.

Two members of the team were taking Ordinary Differential Equations, while another had already completed the course. They were interested in seeing what the mathematics they were learning could do outside the classroom.

As Juarez explains, "We were curious about how the mathematical tools we were learning could be applied to a real-world problem, and MCM felt like the perfect opportunity to put that knowledge to the test."

Juarez had worked on research projects before, but MCM was different. With only four days to work, the team had to move quickly, make decisions together, and figure things out as they went.

Looking Beyond the Battery

The team’s research into smartphone batteries led them into some unexpected areas.

They dug through decades of research, including studies from the 2G and 3G era, and looked at everything from fast charging to battery aging.

Their research also showed that phones below 80% battery capacity are generally considered no longer reliable. That surprised them and led to new questions about the choices manufacturers make about battery life and performance.

Then there was the challenge of building the model itself.  Juarez explains, "The most challenging aspect was accounting for all the external factors that influence battery performance, temperature, altitude, and the general “black box” nature of battery storage." The team had to decide which of those factors they could realistically account for in just four days.

A Mathematical Modeling Student Experience Unlike Any Classroom

The four-day deadline made MCM very different from a regular class.

"It felt like doing full‑scale research, but compressed into just a few days. At times, it reminded me of the urgency researchers faced when modeling COVID‑19 spread and recovery," Juarez said.

For Juarez, much of the mathematics the team used wasn't necessarily new. What was new was having to learn so much about smartphone batteries in such a short amount of time.

The team spent those four days digging into technical literature and deciding what information mattered for the problem they were trying to solve.

As Juarez puts it, "Honestly, the only things we couldn’t have learned in a classroom were the specific facts and findings about smartphone batteries. The competition pushed us to explore technical details that aren’t typically covered in coursework."

That kind of learning became an important part of the experience. The team wasn't just applying mathematics they already knew. They also had to learn enough about an unfamiliar subject to decide how to model it.

Carrying the Experience Into Research

Juarez's mathematical modeling student experience didn't end when the competition was over.

Today, he is participating in a Research Experiences for Undergraduates (REU) program at the University of Kansas through the ARISE program, where he is helping measure community resilience to natural disasters and severe weather.

Rather than simply analyzing someone else's work, Juarez and his research partner wanted to build their own models. "My colleague and I even asked if we could model the problem ourselves, and I have already built both simple and panel regressions. I'm excited to keep applying what I learned."

For Juarez, the MCM experience also influenced the research he pursued next.

Advice for Future Competitors

Juarez encourages students who aren't sure whether to participate to simply give it a try.

Students may be surprised by how much they can accomplish in just four days, he says, from discovering what their team is capable of to seeing how their effort translates into results. And despite the intensity of the competition, Juarez says students can genuinely have fun along the way.

Perhaps most importantly, Juarez suggested that "You don't need deep mathematical expertise; you can bring strengths from many different fields."

For Juarez and his teammates, those four days showed them what they could accomplish by working together on a problem they had never seen before.

And his team isn't alone. At IU South Bend, a first-time MCM/ICM team sparked more students becoming interested in mathematical modeling, while another first-time MCM team continued exploring its models and new techniques after the competition ended. Each experience was different, but all show how four days of modeling can become the beginning of something much bigger.

Learn more about the Mathematical Contest in Modeling, and consider joining the next competition.