The Glucose Problem (Part II). Glucose is a simple sugar that serves as an energy source in organisms. Scientists have determined that glucose absorption from the gas- trointestinal tract (GI tract) in rats and rabbits can be modeled by the exponential function P(t) = 1– e“, a < 0. •t is time in hours • a is a constant P is the fraction of glucose absorbed by the GI tract and in this case the range of P is [0, 1]. When P = 1, that means that all glucose has been completely absorbed, when P = } half of the glucose has been absorbed, and when P = 0 none of the glucose has been absorbed. (a) Find dP Use the formula – (e**) = kekt. dt dt (b) Can you write the derivative in terms of just a and P? Hint: Use the given function for P(t) and some algebra. dP in the context of rats and rabbits (c) Using what you found in part (b), interpret absorbing glucose. How does the function P(t) behave in the long term? Why does it behave that way? dP (d) Is always positive, always negative, or sometimes positive and sometimes dt negative? What does that mean for the rate-of-change of the glucose?
The Glucose Problem (Part II). Glucose is a simple sugar that serves as an energy source in organisms. Scientists have determined that glucose absorption from the gas- trointestinal tract (GI tract) in rats and rabbits can be modeled by the exponential function P(t) = 1– e“, a < 0. •t is time in hours • a is a constant P is the fraction of glucose absorbed by the GI tract and in this case the range of P is [0, 1]. When P = 1, that means that all glucose has been completely absorbed, when P = } half of the glucose has been absorbed, and when P = 0 none of the glucose has been absorbed. (a) Find dP Use the formula – (e**) = kekt. dt dt (b) Can you write the derivative in terms of just a and P? Hint: Use the given function for P(t) and some algebra. dP in the context of rats and rabbits (c) Using what you found in part (b), interpret absorbing glucose. How does the function P(t) behave in the long term? Why does it behave that way? dP (d) Is always positive, always negative, or sometimes positive and sometimes dt negative? What does that mean for the rate-of-change of the glucose?
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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Please answer all parts to the question, and please show the solution so I can understand.
![The Glucose Problem (Part II). Glucose is a simple sugar that serves as an energy
source in organisms. Scientists have determined that glucose absorption from the gas-
trointestinal tract (GI tract) in rats and rabbits can be modeled by the exponential
function
P(t) = 1– e“, a < 0.
•t is time in hours
• a is a constant
P is the fraction of glucose absorbed by the GI tract and in this case the range
of P is [0, 1]. When P = 1, that means that all glucose has been completely
absorbed, when P = } half of the glucose has been absorbed, and when P = 0
none of the glucose has been absorbed.
(a) Find
dP
Use the formula – (e**) = kekt.
dt
dt
(b) Can you write the derivative in terms of just a and P? Hint: Use the given
function for P(t) and some algebra.
dP
in the context of rats and rabbits
(c) Using what you found in part (b), interpret
absorbing glucose. How does the function P(t) behave in the long term? Why
does it behave that way?
dP
(d) Is
always positive, always negative, or sometimes positive and sometimes
dt
negative? What does that mean for the rate-of-change of the glucose?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f597e92-9e6c-41a2-88fa-8651d8bc4923%2F92b564b3-10c6-4b92-8378-8102ad719cab%2Fy9bho2p.png&w=3840&q=75)
Transcribed Image Text:The Glucose Problem (Part II). Glucose is a simple sugar that serves as an energy
source in organisms. Scientists have determined that glucose absorption from the gas-
trointestinal tract (GI tract) in rats and rabbits can be modeled by the exponential
function
P(t) = 1– e“, a < 0.
•t is time in hours
• a is a constant
P is the fraction of glucose absorbed by the GI tract and in this case the range
of P is [0, 1]. When P = 1, that means that all glucose has been completely
absorbed, when P = } half of the glucose has been absorbed, and when P = 0
none of the glucose has been absorbed.
(a) Find
dP
Use the formula – (e**) = kekt.
dt
dt
(b) Can you write the derivative in terms of just a and P? Hint: Use the given
function for P(t) and some algebra.
dP
in the context of rats and rabbits
(c) Using what you found in part (b), interpret
absorbing glucose. How does the function P(t) behave in the long term? Why
does it behave that way?
dP
(d) Is
always positive, always negative, or sometimes positive and sometimes
dt
negative? What does that mean for the rate-of-change of the glucose?
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