Just as a heads up: this is a homework question, so I would prefer guidance as opposed to a definitive answer.
The question poses that an oven is preheated to a constant temperature. A thermometer is placed inside starting at $26^\circ$C. After $40$ seconds the thermometer reads $32^\circ$C, and after $80$ it reads $33^\circ$C. How hot is the oven?
The class is differential equations, so I would presume it expects the use of the heat equation. I'm just not sure where to start. We also haven't started PDEs yet so I'm not sure how we are expected to answer this. It expects an answer to $2$ decimals.
Best Answer
You are presumably expected to assume the reading of the thermometer rises at a rate proportional to the temperature difference of the oven and the thermometer. Write the differential equation with an unknown constant of proportionality. Solve the equation, then use the data points to evaluate the constant. The result should exponentially approach the oven temperature.