Answer:
Step-by-step explanation:
add a picture of the question please
Answer:
53.3324
Step-by-step explanation:
given that a thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 40° F.
By Newton law of cooling we have
T(t) = ![T+(T_0-T)e^{-kt}](https://tex.z-dn.net/?f=T%2B%28T_0-T%29e%5E%7B-kt%7D)
where T (t) is temperature at time t,T =surrounding temperature = 40, T0 =70 = initial temperature
After half minute thermometer reads 60° F. Using this we can find k
![T(0,5) = 40+(70-40)e^{-k/2} = 60\\e^{-k/2} =2/3\\-k/2 = -0.4055\\k = 0.8110](https://tex.z-dn.net/?f=T%280%2C5%29%20%3D%2040%2B%2870-40%29e%5E%7B-k%2F2%7D%20%3D%2060%5C%5Ce%5E%7B-k%2F2%7D%20%3D2%2F3%5C%5C-k%2F2%20%3D%20-0.4055%5C%5Ck%20%3D%200.8110)
So equation is
![T(t) = 40+(30)e^{-0.8110t}\\](https://tex.z-dn.net/?f=T%28t%29%20%3D%2040%2B%2830%29e%5E%7B-0.8110t%7D%5C%5C)
When t=1,
we get
![T(1) = 40+(30)e^{-0.8110}\\\\=53.3324](https://tex.z-dn.net/?f=T%281%29%20%3D%2040%2B%2830%29e%5E%7B-0.8110%7D%5C%5C%5C%5C%3D53.3324)
Answer: 6 boxes. average 45 each.
Step-by-step explanation: