1. 7-4 Exponential Growth and Decay

2. Newton’s Law of Cooling: T – TS = (T0 – TS)e–kt
Ex 7) A temperature probe (thermometer) is removed from a cup of coffee and placed in water that has a temperature of TS = 4.5° C. Temperature readings T, as recorded in the table, are taken after 2 sec, 5 sec, and every 5 sec thereafter. Estimate:
a) The coffee’s temperature at the time the temperature probe was removed.
b) The time when the temperature probe reading will be 8°C.
Time (sec)
T (°C)
T – TS (°C) 2
64.8
60.3 5
49.0
44.5 10
31.4
26.9 15
22.0
17.5 20
16.5
12.0 25
14.2
9.7 30
7.5
Newton’s Law of Cooling:
T – TS = (T0 – TS)e–kt
T – 4.5 = (T0 – 4.5)e–kt
(need this 3rd column which is 2nd column – 4.5) L1 L2
Use calculator to calculate an exponential regression
STAT  CALC  0: ExpReg

3. y = abx  a = b = .928
Now T – 4.5 = (61.656)(.928)t
T = (61.656)(.928)t
Check it! STAT PLOT 1-ON, 1st type, X: L1, Y: L2
WINDOW: [0, 30] x [0, 65] (Scale = 5)
Y1 = (61.656)(.928)t
Coffee’s temp when thermometer removed
T = (61.656)(.928)0 = °
Time thermometer reads 8° C
Graph Y2 = 8 and find intersection
t =  38 sec
(need to adjust window)

4. homework
Pg. 361 # 1, 2, 4, 5, 7, 8, 22, 25, 33