Question

If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference between the temperature of the oven and the temperature of the object decreases exponentially with time. The percentage rate of decrease depends on the material that is being heated. Suppose a potato initially has a temperature of 75 degrees and the oven is preheated to 375 degrees. Use the formula
D = 300 � 0.98t,
where D is the temperature difference between the oven and the potato, t is the time in minutes the potato has been in the oven, and all temperatures are measured in degrees Fahrenheit.
What is the temperature of the potato after 20 minutes? (Round your answer to the nearest degree.)
- I'm slightly confused by this problem because when I put D=300 times 0.98^20 it gives me 200 and it says this answer is wrong. What am I doing wrong is 20 not what i plug in for t?

Answer 1

Answer:

  potato temperature: 175 degrees

Step-by-step explanation:

You have to read all the words.

The formula is for the difference in temperature between oven temperature and potato temperature. Your calculation of 200 degrees difference is correct. Now you need to convert that to the potato temperature by subtracting that difference from the oven temperature of 375 degrees:

  oven temp - temp difference = potato temp

  375 - 200 = 175 = potato temperature