Question

A cup of coffee is served at 150 degrees Fahrenheit and is left in a room that is 70 degrees Fahrenheit. Suppose that when the coffee is first placed in the room it is cooling at a rate of 20 degrees per minute. How long does it take for the coffee to cool to 100 degrees?
A. 2 ½ minutes
B. 3 minutes
C. 4 minutes
D. 4 ½ minutes

Answer 1

you can use newtons law of cooling here

Answer 2

A

Answer 3

fan and medal because 20*2.5 is 50 150-50=100 @kiker

Answer 4

so wait how is it a?

Answer 5

this is really a differential equation problem.
Let
T(t) = temperature of object at time t
T(0)= T_o =initial temperature of object
T_a = ambient temperature

Answer 6

\[\frac{dT}{dt} = -k(T-T_a)\]

Answer 7

This has the solution
\[T(t)=T_a + (T_o-T_a)e^{-kt} \]

Answer 8

I'm learning this too
would it be
ln(3/8) / 20 = 0.049 = 2.9 minutes
so would it be B?

Answer 9

\[T(t)=T_a + (T_o-T_a)e^{-kt} \\ \text{this gives us} \\ T(t) = 70 + 80e^{-kt}\]

Answer 10

ok so far?

Answer 11

they gave cooling at 20 degrees per minute...

Answer 12

ohhh

Answer 13

ln(3/4) = 0.28768 = k?

Answer 14

there is a problem very similar to this one here:
https://math.dartmouth.edu/~klbooksite/3.02/302examples/302coffee.htm

Answer 15

just change the 170 degrees to 150 degrees

Answer 16

I would do the problem over again, but i am experiencing terrible lag.