Concept explainers
Concentration of Glucose in the Bloodstream A glucose solution is administered intravenously into the bloodstream at a constant rate of r mg/hr. As the glucose is being administered, it is converted into other substances and removed from the bloodstream. Suppose the concentration of the glucose solution at time t is given by
where C0 is the concentration at time t = 0 and k is a positive constant. Assuming that C0 < r/k, evaluate
- a. What does your result say about the concentration of the glucose solution in the long run?
- b. Show that the function C is increasing on (0, ∞).
- c. Show that the graph of C is concave downward on (0, ∞).
- d. Sketch the graph of the function C.
Trending nowThis is a popular solution!
Chapter 5 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- Flea Beetles A study of flea beetles found that the change in the rate of flea beetles moving in and out of a patch of beetles could be described by the differential equation dNdt=mN+i where N is the number of beetles in a patch, m is the rate at which beetles move out of the patch, and i is the rate at which they move in. Source: Ecological Monographs. a. Solve the differential equation above with the initial condition N(0)=N0. b. After the researchers cleared a patch of beetles, so that N0, they would return 8 hours later and count the number of beetles. Show that the parameter i can then be estimated by the equation i=mN(8)e8m1 c. The researchers estimated m using the equation m=lnFsd, where Fsd is the fraction of beetles who remained in the patch in which they were released. For the beetles P, striolata released in July in the lush interior of patches 5 meters apart, the average values of Fsd and N(8) were 0.709 and 4.5, respectively. Find the values of m and i.arrow_forwardPlant Growth Researchers have found that the probability P that a plant will grow to radius R can be described by the differential equation dPdR=4DRP2 where D is the density of the plants in an area. Source: Ecology. Given the initial condition P(0)=1, find a formula for P in term of R.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning