Question

A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit.
(a) If the temperature of the turkey is 159 Fahrenheit after half an hour, what is its temperature after 45 minutes?
Your answer is Fahrenheit.
(b) When will the trukey cool to 100 Fahrenheit?
Your answer is hours.

I searched for the solution everywhere and I tried using them but I still can't seem to find the right answer.. Please help me!!

Answer 1

ok first we have to work not with the temperatures, but with the difference between the heated temp and the room temp, initially that difference is \(185-75=110\) degrees so we work with that number

Answer 2

after 30 minutes the difference in the temperatures is \(159-75=84\) degrees. so now we can set up our equation using the numbers \(110, 84,\) and \(30\) since the time is 30 minutes later

Answer 3

the equation for the difference between the room temp and the heated temp will be
\[110\times \left(\frac{84}{110}\right)^{\frac{t}{30}}\] where t is time

Answer 4

we can clean this up a little and make it
\[110\left(\frac{42}{55}\right)^{\frac{t}{30}}\] replace \(t\) by \(45\) and get
\[110\left(\frac{42}{55}\right)^{\frac{45}{30}}\]
\[=110\left(\frac{42}{55}\right)^{1.5}\] and then a calculator, but remember this is the difference in the temperatures, so to get your answer you have to add 75 to the result

Answer 5

if you were supposed to use something like
\[e^{-kt}\] we can do that too but it is unnecessary and annoying because you have to find \(k\) first. notice we just used the numbers given to us

Answer 6

i get 73.4 but you have to add 75 to that, so it is 148.4
http://www.wolframalpha.com/input/?i=110%2842%2F55%29^%281.5%29

Answer 7

think i lost donnac10, but that is ok

Answer 8

Aww... I'm so sorry.. My computer was dying and the charger was acting up so I had to fix it.. Thanks sooo much for your help! I'll try them now.. :D