At time t = 0, a tank contains 100 liters of water. The piecewise - linear graph below shows the rate R(t), in liters per minute, at which water is being pumped into the tank during a 55 minute period. R() (20, 30) (35, 30) 30- 20- 10 (0, 10) (55, 0) 0+ 10 20 30 40 50 Time (minutes) a). How many liters of water have been pumped into the tank from time t =0 to time t = 55 minutes? Show the work that leads to your answer. (sin t) b). At time t = 10 minutes, water begins draining from the tank at a rate modeled by the function D, where D (t) = 10e 10 liters per minute. Water continues to drain at this rate until time t = 55 minutes. How many liters of water have drained from the tank from time t =0 to time t = 55 minutes? Set up a definite integral to represent this situation, and use a graphing calculator/desmos to evaluate the definite integral. Round or truncate answer to 3 decimal places. c). How many liters of water in the tank at time t = 55 minutes? Show the work that leads to your answer. Round or truncate answer to 3 decimal places. d). Using the functions R and D, determine whether the amount of water in the tank is increasing or decreasing at time t = 45 minutes. Justify your answer. Rate (liters per minute)

At time t = 0, a tank contains 100 liters of water. The piecewise - linear graph below shows the rate R(t), in liters per minute, at which water is being pumped into the tank during a 55 minute period. R() (20, 30) (35, 30) 30- 20- 10 (0, 10) (55, 0) 0+ 10 20 30 40 50 Time (minutes) a). How many liters of water have been pumped into the tank from time t =0 to time t = 55 minutes? Show the work that leads to your answer. (sin t) b). At time t = 10 minutes, water begins draining from the tank at a rate modeled by the function D, where D (t) = 10e 10 liters per minute. Water continues to drain at this rate until time t = 55 minutes. How many liters of water have drained from the tank from time t =0 to time t = 55 minutes? Set up a definite integral to represent this situation, and use a graphing calculator/desmos to evaluate the definite integral. Round or truncate answer to 3 decimal places. c). How many liters of water in the tank at time t = 55 minutes? Show the work that leads to your answer. Round or truncate answer to 3 decimal places. d). Using the functions R and D, determine whether the amount of water in the tank is increasing or decreasing at time t = 45 minutes. Justify your answer. Rate (liters per minute)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

At time t = 0, a tank contains 100 liters of water. The piecewise - linear graph below shows the rate R(t), in liters per minute, at which water is being
pumped into the tank during a 55 minute period.
R(1)
(20, 30)
(35, 30)
30-
20-
10 (0, 10)
(55, 0)
10
20
30
40
50
Time (minutes)
a). How many liters of water have been pumped into the tank from time t =0 to time t = 55 minutes? Show the work that leads to your answer.
(sin t)
b). At time t = 10 minutes, water begins draining from the tank at a rate modeled by the function D, where D (t) = 10e 10 liters per minute. Water
continues to drain at this rate until time t = 55 minutes. How many liters of water have drained from the tank from time t = 0 to time t = 55 minutes? Set
up a definite integral to represent this situation, and use a graphing calculator/desmos to evaluate the definite integral. Round or truncate answer to 3
decimal places.
c). How many liters of water in the tank at time t = 55 minutes? Show the work that leads to your answer. Round or truncate answer to 3 decimal
places.
d). Using the functions R and D, determine whether the amount of water in the tank is increasing or decreasing at time t = 45 minutes. Justify your
answer.
Rate
(liters per minute)

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