This involves Enthalpy of Neutralization: A student determined the calorimeter constant of the calorimeter. Using a plotted line. The student added 50ml of cold water to 50 ml of heated water in a Styrofoam cup. The initial temperature of the cold water was 21 degree C, the temperature of the hot water is 29.15 degree C. The maximum temp. of the mixture was found to be 24.81 degree C. Assume the density of water is 1.00g ml^-1 and the specific heat is 4.184 J g^-1 K^-1. Determine the change in T for the hot and cold water. If I get this wrong, the next 12 questions on the lab are wrong! HELP

You don't have any unknowns to solve for.
The temperature of the cold water changed from 21.0 to 24.81 and the temperature of the hot water changed from 29.15 to 24.81. So what's the question?

I was confused because of the wording of the problem, 24.81 is the maximum temp., so do I assume that is the FINAL temp. therefore using the formula
Change in Temp = Tinitial - T final?
I know this sounds trivial, but I'm just not sure?

No worries, I can clarify that for you. In this case, you are correct to assume that the maximum temperature of 24.81 °C is the final temperature of the mixture. In order to determine the change in temperature for the hot and cold water, you can use the formula:

Change in temperature = Final temperature - Initial temperature

For the cold water, the initial temperature is 21.0 °C and the final temperature is 24.81 °C. Plugging these values into the formula, you get:

Change in temperature (cold water) = 24.81 °C - 21.0 °C

Similarly, for the hot water, the initial temperature is 29.15 °C and the final temperature is also 24.81 °C. Plugging these values into the formula, you get:

Change in temperature (hot water) = 24.81 °C - 29.15 °C

Now you can calculate these changes in temperature to find the answers.