Posted by **Hannah** on Monday, November 22, 2010 at 9:57pm.

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?

- Math -
**Reiny**, Monday, November 22, 2010 at 10:32pm
You will need Newton's Law of Cooling formula, which is

T(t) = T_{m} + (T_{0} - T_{m})e^(kt)

where T(t) is the current temperature of the object

T_{m} is the surrounding temperature and

T_{0}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

- Math -
**Hannah**, Tuesday, November 23, 2010 at 9:05pm
Thank you!!!

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