circumference from dia y kate Mosley 1st PreAP PreCalculus Emily Kate Mosley Hom
ID: 2912461 • Letter: C
Question
circumference from dia y kate Mosley 1st PreAP PreCalculus Emily Kate Mosley Homework: APPLICATION - Interest, Exp Law, Cooling, L Score: 0 of 1 pt 12 of 14 (10 complete) HW Score: Instructor-created question A thermometer reading 90C is brought into a room with a constant temperature of 33°C. (a) If the thermometer reads 13 C after 3 minutes, what will it ead after being in the room for 5 minutes? For 10 minutes? (a) After 5 minutes, the thermometer will read approximately c. Round to the nearest hundredth as needed.) After 10 minutes, the thermometer ill rad approximatelyc (Round to the nearest hundredth as needed)Explanation / Answer
Newtons law of coolin' wil work here :
T(t) = Ta + (Th - Ta)e^(-kt)
where,
T(t) = Temperature at time t,
TA = Ambient temperature (temp of surroundings),
TH = Temperature of hot object at time 0,
k = positive constant and
t = time.
We have
T = 33 + (9 - 33)e^(-kt)
T = 33 - 24e^(-kt)
Given when t = 3, T = 13 :
13 =33 - 24e^(-3k)
20/24 = e^(-3k)
ln(20/24) = -3k
So, k = 0.0607738522646515
So,
T = 33 - 24e^(-0.060774t)
a)
5 min :
T = 33 - 24e^(-0.060774*5)
15.29 degrees ----> ANS
b) 10 min :
T = 33 - 24e^(-0.060774*10)
19.93 ----> ANS
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