You place a cup of 205F coffee on a table in a room that is 72F, and 10 minutes later, it is 195F. Approximately how long will it be before the coffee is 180F?

Question

anonymous · Answer

there are a couple ways to do this but either way works with the difference in the temperatures, not the temperatures
in other words work with $205-72=133$ and $195-72=123$

anonymous · Answer

the easy way is to say that since it takes 10 minutes for the temp difference to go from 133 to 123
then you can model it as 
$$T=133\times \left(\frac{123}{133}\right)^{\frac{t}{10}}$$

anonymous · Answer

when the coffee is $180$ degrees then the temperature difference is $180-72=108$ and you can solve by setting 
$$108=133\times \left(\frac{123}{133}\right)^{\frac{t}{10}}$$ and solve for $t$

anonymous · Answer

im so bad at math.. how would i get t?

anonymous · Answer

the other way is to use 
$$T=T_0e^{kt}$$ which may be what you are taught, but then you have to solve for $k$ first
is that what you are supposed to do? or are you just supposed to get the answer?

anonymous · Answer

25 mins!

anonymous · Answer

i got it thank you.

anonymous · Answer

ok good, but i get 26.6 about, 
if you are just approximating then 25 is close

anonymous · Answer

yw