Asked by Hannah

An object is heated to 90 degrees Celcius and is then allowed to cool in a room whose air temperature is 25 degrees celcius. If the temperature of the object is 75 degrees celcius after 10 minutes, when will its temperature be 50 degrees celcius?
Answered by Reiny
You will need Newton's Law of Cooling formula, which is
T(t) = T<sub>m</sub> + (T<sub>0</sub> - T<sub>m</sub>)e^(kt)

where T(t) is the current temperature of the object
T<sub>m</sub> is the surrounding temperature and
T<sub>0</sub>is the starting temperature
t is in minutes, and k is a constant

first we have to find the value of k

75 = 25 + (90-25)e^(10k)
50 = 65 e^(10k)
.76923 = e^(10k)
10k = ln .76923
k = -.026236

so now
50 = 25 + (90-25)e^(-.026236t)
25/65 = e^(-.026236t)
(-.026236t) = ln(25/65)
t = 36.42 minutes
Answered by Hannah
Thank you!!!
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