Murder Mystery Timeline

Differential Equations · Axiom Academy

A body is found cooling toward room temperature. Two thermometer readings, one differential equation, and no need to guess how fast it cools. Newton's Law of Cooling says a body's temperature decays exponentially toward the room around it — take two readings a known time apart, and you can back-solve for the cooling rate AND the moment of death, with no assumptions. Run the investigation yourself. A body cools on one curve, every time Drag time forward and watch body temperature fall from 98.6°F toward the room's 68°F — fast at first, then slower and slower as the gap closes. That's : the cooling RATE is proportional to how far above room temperature the body still is. Two readings, no guessing — solve for the timeline The detective takes a temperature reading, waits exactly one hour, and takes a second. That's enough — k and the time of death both fall out, with nothing assumed. Step through the case's actual numbers. A thermometer only reads so precisely — how much does that matter? Every reading carries some error. Drag the thermometer's precision and watch the time-of-death estimate stop being one exact instant and become a WINDOW — this is why medical examiners report a range, not a single minute.

This is the written version of the interactive lesson above. See the full Differential Equations course.