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Derivative word problem - have I got the wrong solution?

linapril

New member
Dec 21, 2012
23
My answer is wrong according to the book, but I don't see where my mistake was made..

The question:
The temperature of a steak that's being put into the oven can be describe with
T(x) = 175-153e-kx
where T(x) is the temperature in degrees Celsius t minutes after the steak has been put into the oven. After 30 minutes the steak's temperature is 50 degrees Celsius. At which rate is the temperature changing then?

This is my solution:
T(30)=50
50=175-153e-50k
-125=-153e-50k
125/153 = e-50k
ln (125/153) = -50k
k = ln(125/153)/-50, approximately 0.004

T(x)=175-153e-0.004x
T'(x)=0.612e-0.004x
T'(30)=0.612e-0.004(30), approximately 0.54

Answer: the steak's temperature is changing by 0.54 degrees Celsius/min, after 30 minutes

Would really appreciate feedback on this!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
You have let the time be 50, rather than 30 minutes in your computation of $k$.
 

linapril

New member
Dec 21, 2012
23
Thank you, MarkFL!