1 A casserole baked at 475 degrees Fahrenheit F is removed f

1. A casserole baked at 475 degrees Fahrenheit (F) is removed from the oven at 6:00 pm into a room that is a constant 60 degrees F. After 5 minutes, the casserole is at 300 degrees F. a. At what time can you begin eating the casserole if you want its temperature to be 140 degrees F? b. Determine the time that would elapse before the casserole is 200 degrees F. c. What is the horizontal asymptote of your casserole temperature function, and what does it tell you about the temperature as time passes?

Solution

Usine Newtons law of cooling :

T(t) = Ts + (To -Ts)e^(-kt)

T_sis the surrounding temperature = 60 degF
T_ois the initial temperature of the body, = 475 degF

k is the constant.

t = 5 min. T(5) = 300

find k : 300 = 60 +(475 -60)e^(-5k)

0.578 = e^(-5k)

take natural log on both sides:

ln(0.578) = -5k

k =0.109

a) T(t) = 140

140 = 60 +(475 -60)e^(-0.109t)

1.646 = e^(-0.109t)

take log on both sides:

ln(1.646) = -0.109t

t = 4.57 minutes

b)T(t) = 200 degF

200 = 60 +(475 -60)e^(-0.109t)

1.0866 = 0.109t

t = 9.7 minutes

c) Horizontal asymtote = 60

It means as time passes temp. of casserole will reach atmospheric temp.