Exponential functions appear in many situations in ordinary life. For this activity, you will gather some data about how long it takes a cup of cold water to warm up.
1. Get a cup of refrigerated water. Use a thermometer to measure the temperature. Allow some time for the thermometer to reach the temperature of the water. Then start timing and recording data as follows:
2. As you record your data, enter it into your graphing calculator. Enter the temperature as degrees below room temperature. If room temperature is 70° and the water temperature is 40°, enter 30° as your temperature.
3. Once you have at least 10 - 15 minutes of data, plot your data and find the best-fit exponential function:
y = a * bx
4. Write up your data, your graph, and your best-fit function neatly on a separate sheet of paper.