6. Let A(t) be the amount of caffeine (in mg) in the bloodstream t hours after a cup of coffee has been consumed (see figure). dA a. What does A'(t)= yA represent? dt 100 80 y = A(t) 60 40 b. Use the graph to estimate the values of A'(7) and A'(15), rounding answers to the nearest whole number. Include units in your answers and interpret meaning of these values in the context of the function. 20 0. 8. 12 16 Time (hours) 4 20 Amount of caffeine (mg)

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Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
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6. Let A(t) be the amount of caffeine (in mg) in the bloodstream t hours after a cup of coffee has
been consumed (see figure).
dA
a. What does A'(t)=
y A
represent?
dt
100
80
y = A(t).
60
40
b. Use the graph to estimate the values of A'(7)
and A'(15), rounding answers to the nearest
whole number. Include units in your answers
20
and interpret meaning of these values in the
context of the function.
0.
4
12
16
Time (hours)
Amount of caffeine (mg)
20
Transcribed Image Text:6. Let A(t) be the amount of caffeine (in mg) in the bloodstream t hours after a cup of coffee has been consumed (see figure). dA a. What does A'(t)= y A represent? dt 100 80 y = A(t). 60 40 b. Use the graph to estimate the values of A'(7) and A'(15), rounding answers to the nearest whole number. Include units in your answers 20 and interpret meaning of these values in the context of the function. 0. 4 12 16 Time (hours) Amount of caffeine (mg) 20
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