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?

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.