Worksheet 6.1 - Integral As Net Change - Calculus Maximus Page 9
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9Calculus Maximus
WS 6.1: Integral as Net Change
12. AP-2011-2
t
0
2
5
9
10
(minutes)
H t
( )
66
60
52
44
43
(degrees Celsius)
t
As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for 0
,
10
where time t is measured in minutes and temperature
H t is measured in degrees Celsius. Values of
H t at selected values of time t are shown in the table above.
(a) Use the data in the table to approximate the rate at which the temperature of the tea is changing at time
t
3.5
. Show the computations that lead to your answer.
10
1
(b) Using correct units, explain the meaning of
H t dt
in the context of this problem. Use a
10
0
10
1
trapezoidal sum with the four subintervals indicated by the table to estimate
H t dt
.
10
0
10
(c) Evaluate
. Using correct units, explain the meaning of the expression in the context of this
H t dt
0
problem.
t , biscuits with temperature 100 C were removed from an oven. The temperature of the
(d) At time
0
biscuits at time t is modeled by a differentiable function B for which it is known that
t
0.173
t
B t
13.84
e
. Using the given models, at time
10
, how much cooler are the biscuits than
the tea?
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