Answer precalculus word problem.

Mathematics
Tutor: None Selected Time limit: 1 Day

If u pour a cup of coffee that is 200 degress F, and set it on a desk in a room that is 68 degrees F, & 10 minutes later it is 145 degres F, what tempetrature will it be 15 min after u originally poured it?

please say step by step 

Aug 30th, 2015

Thank you for the opportunity to help you with your question!

if you lost 55 degrees in 10 min you would loose 5.5 degrees in 1 min then you multiply by 15. 15* 5.5 = 82.5 degrees then you subtract from 200. 200-82.5 = 117.5 degrees in 15 min <--------Answer

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 30th, 2015

i got 127 degrees, using the formula T=Ambient temp +(original temp -ambeint temp)e^-kt 

Aug 30th, 2015

i got 127 degrees, using the formula T=Ambient temp +(original temp -ambeint temp)e^-kt 

Aug 30th, 2015

But if you think it logically, my above calculations would be correct. Not using newton's law of cooling.

Aug 30th, 2015

can you do it using newtons law of cooling, that is how my teacher wants it to be done 

Aug 30th, 2015

K let me try it using Newton's law of cooling.

Aug 30th, 2015

Hi,

    So here is the step by step explanation for your question:

Newton's Cooling Law: T(a)=Ce^(-kt)+Ta

Step 1:

T(a): 68F

T(0): 200F

T(10): 145F

T(15): ?

Step 2:

T(0): 200F

200 = Ce^(-k*0)+68

C = 132

Step 3:

T(10) = 132e^(-10k)+68

145-68 = 132e^(-10k)

77/132 = e^(-10k)

Taking natural log

k = 0.0538

Step 4:

T(15) = 132e^(-0.0538*15)+68

=126.872F

Answer = Temperature after 15 min: 126.872F

Hope I was helpful my friend, please revert if you have more questions. I would love to help you more.

Aug 30th, 2015

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