The temperature of a room, in degrees Fahrenheit, on a certain day is modeled by the function f defined at the right, where g is a differentiable function and tis measured in hours since midnight. Values of g(t) at selected values of t are given in the table at the right. f(t) = g (t) -3t+83 t (hours) g(t) (degrees Fahrenheit) for 0 ≤ t ≤ 12 for 12 < t < 24 0 4 87 81.5 6 76 a. According to the data table of f what is the average rate of change of temperature of the room over the time interval 0 ≤ t ≤ 12 hours? b. Isf continuous for 0 ≤ t ≤ 24 hours? Justify your answer. in degrees c. Find f'(20), the instantaneous rate of change in the temperature of the room, Fahrenheit per hour, at time t = 20 hours. Interpret your answer in context using one sentence. 8 70.5 12 65
The temperature of a room, in degrees Fahrenheit, on a certain day is modeled by the function f defined at the right, where g is a differentiable function and tis measured in hours since midnight. Values of g(t) at selected values of t are given in the table at the right. f(t) = g (t) -3t+83 t (hours) g(t) (degrees Fahrenheit) for 0 ≤ t ≤ 12 for 12 < t < 24 0 4 87 81.5 6 76 a. According to the data table of f what is the average rate of change of temperature of the room over the time interval 0 ≤ t ≤ 12 hours? b. Isf continuous for 0 ≤ t ≤ 24 hours? Justify your answer. in degrees c. Find f'(20), the instantaneous rate of change in the temperature of the room, Fahrenheit per hour, at time t = 20 hours. Interpret your answer in context using one sentence. 8 70.5 12 65
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 46SE: Near the surface of the moon, the distance that an object falls is a function of time. It is given...
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See the attached problem in Calculus.
Transcribed Image Text:The temperature of a room, in degrees Fahrenheit, on
a certain day is modeled by the function f defined at
the right, where g is a differentiable function and t is
measured in hours since midnight. Values of g(t) at
selected values of t are given in the table at the right.
f(t):
www
g(t)
for 0 <t≤ 12
- 3t+83 for 12 < t < 24
-
t (hours)
g(t) (degrees Fahrenheit)
0
87
81.5
6
76
According to the data table of f what is the average rate of change of temperature of the
room over the time interval 0 ≤ t ≤ 12 hours?
a.
b. Is fcontinuous for 0 ≤ t ≤ 24 hours? Justify your answer.
c. Find f'(20), the instantaneous rate of change in the temperature of the room, in degrees
Fahrenheit per hour, at time t = 20 hours. Interpret your answer in context using one
sentence.
8
70.5
12
65
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