SOLUTION: A cake is removed from an oven at 325 degrees F and cools to 150 degrees F after 25 minutes in a room 68 degrees F. How long will it take the cake to cool to 109 degrees F? 150=

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A cake is removed from an oven at 325 degrees F and cools to 150 degrees F after 25 minutes in a room 68 degrees F. How long will it take the cake to cool to 109 degrees F? 150=      Log On


   

Question 1036687: A cake is removed from an oven at 325 degrees F and cools to 150 degrees F after 25 minutes in a room 68 degrees F. How long will it take the cake to cool to 109 degrees F?
150=68+257e^-25k
82=257e^-25k
.001242=e^-25k
-25k=ln(.001242)
k=.267
I know it's wrong, but I don't know where I went wrong
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What you did is the right start. I think they want
you to find +k+ ( which you did ), then
resolve the equation and find the new multiplier
with +k+ for cooling to 109 degrees F
--------------------------------------
I'll check what you did first:
+150+=+68+%2B+257%2Ae%5E%28-25k%29+
+82+=+256%2Ae%5E%28+-25k+%29+
+.3203125+=+e%5E%28-25k%29+
+ln%28+.3203125+%29+=+-25k+
+-1.13846+=+-25k+
+k+=+.045538+
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Let the multiplier of +k+ = x
Now solve this equation:
+109+=+68+%2B+257%2Ae%5E%28-x%2Ak%29+
+41+=+257%2Ae%5E%28-x%2Ak%29+
+.159533+=+e%5E%28-x%2Ak%29+
+ln%28+.159533+%29+=+-x%2Ak+
+-1.8355+=+-x%2A.045538+
+x+=+40.3071+
and
+.3071%2A60+=+18.426+
-----------------------
It takes about 40 min and 18 sec for
the cake to cool to 109 degrees F
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Check my math, and you may want a
2nd opinion, too