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College Algebra Newton's law of Cooling...HELP!?
Suppose the room temperature of 67 degree, and the temperature of a cup of coffee is 167 degrees, when it is placed on the the table. In 7 minutes the coffee cools to 157 degrees. Use Newton's Law of cooling to determine how long it will take for the coffee to cool to 122 degress. Round your answer to 2 decimal places. PLEASE HELP :(
1 Answer
- M3Lv 78 years agoFavorite Answer
if you study newton's law carefully, you will realize that all it says in effect is that the DIFFERENCE in temperature from ambient decays exponentially
difference becomes 90/100 ie 0.9 times in 7 minutes
so by the general exponential formula, difference
D = 100*0.9^(t/7)
and to get a difference of 122-67 = 55°
55 = 100*0.9^(t/7)
0.9^(t/7) = 0.55
t/7 = ln 0.55 /ln 0.9
t = 7*ln 0.55 / ln 0.9 = 39.72 mins <------
