At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by M(t) = 3.85(10 – t)² In(t – 3) for 4

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At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by
司
M(t) = 3.85(10 – t)² In(t – 3) for 4 < t < 10, where M(t) is measured in
muffins
per hour andt is the number of hours since midnight (f = 0). The muffins
are sold from / A.M. to 11 A.M. at a rate modeled by
= 0.014t sin2(0.79(t – 7)) for 7 < t < 11, where S(t) is measured in
S(t)
muffins per hour and f is the number of hours since midnight (f = 0). There are no
muffins in the bakery at 4 A.M.
a. Find S'(8). Using correct units, interpret the meaning of S'(8) in the context of
the problem.
b. Is the number of muffins in the bakery inereasing or decreasing at 9: 30 A.M. (
1%= 9.5)? Explain your reasoning.
C. At what time t, for 7 < < 10, is the number of muffins in the bakery a
maximum? Justify your answer.
d. First, identify which of the following expressions (A, B, C, D, or E) could be used to
determine the number of muffins in the bakery at 11A.M. (I =11) Then provide
the number of muffins in the bakery at 11 A.M. († =
T1). Give your answer to the
nearest whole number.
A. M(10) S(11)
M 110)-М(4)
В.
S(11) – S(7)
10 – 4
.
11 – 7
10
S(t)dt
M(t)dt -
7.
C.
4.
Transcribed Image Text:At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by 司 M(t) = 3.85(10 – t)² In(t – 3) for 4 < t < 10, where M(t) is measured in muffins per hour andt is the number of hours since midnight (f = 0). The muffins are sold from / A.M. to 11 A.M. at a rate modeled by = 0.014t sin2(0.79(t – 7)) for 7 < t < 11, where S(t) is measured in S(t) muffins per hour and f is the number of hours since midnight (f = 0). There are no muffins in the bakery at 4 A.M. a. Find S'(8). Using correct units, interpret the meaning of S'(8) in the context of the problem. b. Is the number of muffins in the bakery inereasing or decreasing at 9: 30 A.M. ( 1%= 9.5)? Explain your reasoning. C. At what time t, for 7 < < 10, is the number of muffins in the bakery a maximum? Justify your answer. d. First, identify which of the following expressions (A, B, C, D, or E) could be used to determine the number of muffins in the bakery at 11A.M. (I =11) Then provide the number of muffins in the bakery at 11 A.M. († = T1). Give your answer to the nearest whole number. A. M(10) S(11) M 110)-М(4) В. S(11) – S(7) 10 – 4 . 11 – 7 10 S(t)dt M(t)dt - 7. C. 4.
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