Question

If your pour a cup of coffee that is 200^0 Fahrenheit and set it on a desk in a room that iis 68 Fahrenheit, and 10 minutes later it is 145 Fahrenheit, what temperature will it be 15 minutes after you originally poured it

Answer 1

not as bad as it looks
ready?

Answer 2

yes

Answer 3

always work with the temperature differences
\[200-68=132\] and
\[145-68=77\]

Answer 4

ok

Answer 5

then without being fancy, you can model the temperature difference as
\[\large 132\times \left(\frac{77}{132}\right)^{\frac{t}{10}}\]

Answer 6

notice i used only the numbers given to you, or rather computed the differences with those numbers
i did not mess around with
\[T=T_0+e^{-kt}\] or whatever

Answer 7

yeah i don''t really like that formula especially since i always forget how to find t

Answer 8

since you want the temperature in fifteen minutes, replace \(t\) by \(15\) and compute
\[132\times \left(\frac{77}{132}\right)^{\frac{15}{10}}\] or
\[132\times \left(\frac{77}{132}\right)^{\frac{3}{2}}\]

Answer 9

then don't forget to add \(68\) to your answer, because that is the difference in the temperatures and you have to add back on the room temp

Answer 10

looks like \(126.8\)
http://www.wolframalpha.com/input/?i=132%2877%2F132%29^%283%2F2%29%2B68