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1 4 5 (minutes) C(t) (ounces) 5.3 8.8 11.2 12.8 13.8 14.5 Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time 1, 0 s i56, is given by a differentiable function C, where t is measured in minutes. Selected values of C(t), measured in ounces, are given in the table above. (a) Use the data in the table to approximate C'(3.5). Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time 1, 2sIS 4, at which C'(t) = 2? Justify your answer. 3,

1 4 5 (minutes) C(t) (ounces) 5.3 8.8 11.2 12.8 13.8 14.5 Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time 1, 0 s i56, is given by a differentiable function C, where t is measured in minutes. Selected values of C(t), measured in ounces, are given in the table above. (a) Use the data in the table to approximate C'(3.5). Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time 1, 2sIS 4, at which C'(t) = 2? Justify your answer. 3,

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.4: Functions Given By Words
Problem 6E
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1 2 5 6 (minutes) C(t) (ounces) 5.3 8.8 11.2 12.8 13.8 14.5 Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time 1, 0si56, is given by a differentiable function C, where t is measured in minutes. Selected values of C(t), measured in ounces, are given in the table above. (a) Use the data in the table to approximate C'(3.5). Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time t, 2 <15 4, at which C'(t) = 2 ? Justify your answer. (c) Use a midpoint sum with three subintervals of equal length indicated by the data in the table to approximate the value of C(t) dt. Using correct units, explain the meaning of C(t) dt in the context of the problem. (d) The amount of coffee in the cup, in ounces, is modeled by B(t) = 16 – 16e-041. Using this model, find the rate at which the amount of coffee in the cup is changing when t = 5. 4. 3.
Transcribed Image Text:1 2 5 6 (minutes) C(t) (ounces) 5.3 8.8 11.2 12.8 13.8 14.5 Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time 1, 0si56, is given by a differentiable function C, where t is measured in minutes. Selected values of C(t), measured in ounces, are given in the table above. (a) Use the data in the table to approximate C'(3.5). Show the computations that lead to your answer, and indicate units of measure. (b) Is there a time t, 2 <15 4, at which C'(t) = 2 ? Justify your answer. (c) Use a midpoint sum with three subintervals of equal length indicated by the data in the table to approximate the value of C(t) dt. Using correct units, explain the meaning of C(t) dt in the context of the problem. (d) The amount of coffee in the cup, in ounces, is modeled by B(t) = 16 – 16e-041. Using this model, find the rate at which the amount of coffee in the cup is changing when t = 5. 4. 3.
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