SOLUTION: 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

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Question 1127616: 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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think the key here is that the temp of the oven
stays at 375 degrees.
Initially:
potato = +75+ degrees
oven = +375+ degrees
D = +375+-+75+=+300+ degrees
--------------------------------------
The formula shows this initial condition
if I let +t=0+
+D%280%29+=+300%2A.98%5E0+
+D%280%29+=+300+
----------------------------
After 20 min:
oven = +375+
+t+=+20+
+D+=+300%2A.98%5E20+
+D+=+300%2A.6676+
+D+=+200.28+
and
+375+-+200.28+=+174.72+
The potato is 175 ( rounded off ) degrees F
if that's not the answer, get a 2nd opinion