calculus

posted by .

A tissue culture grows until it has an area of 9 cm^2. A(t) is the area of the tissue at time t. One model for the growth rate is A'(t)=k*sqrt(A(t))*(9-A(t)) for some constant k. The number of cells on the edge is proportional to sqrt(A(t)) and most of the growth occurs on the edge.

A) How do you show that the maximum rate of growth occurs at any time when A(t)=3 cm^2?

B)Assuming that k=6, then how do you find the solution corresponding to A(0)=1?
and for A(0)=4?

  • calculus -

    Most of the cells are on the edge,so A'=k(sqrt(A)) which implies that growth rate is proportional to diameter.

    growth rate= k(sqrt(A) * (9-A)

    growth rate ' = -ksqrtA+ k/2sqrtA * (9-A)
    set growth rate '=0

    2A=(9-A) or A=3cm^3

  • calculus -

    A)
    dA/dt = k A^.5 (9-A) = 9 k A^.5 -k A^1.5

    d^2A/dt^2 = .5(9)k A^-.5 - 1.5 k A^.5

    when that is 0 we have a max or min
    4.5 /A^.5 = 1.5 A^.5
    A = 4.5/1.5 = 3 done

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Anatomy

    Describe each part of the respiratory passage regarding tissue, and why that tissue would be appropriate for that area. THANK YOU!
  2. human body

    With your understanding of bone and muscle tissue (cells and the extracellular material) discuss two lifestyle factors (one for bone and one for muscle) that affect the growth, development, size and/or healing (positively or negatively) …
  3. structure and function of the human body

    With your understanding of bone and muscle tissue (cells and the extracellular material) discuss two lifestyle factors (one for bone and one for muscle) that affect the growth, development, size and/or healing (positively or negatively) …
  4. Calculus

    The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a …
  5. Calculus (math)

    A bacteria culture grows with constant relative growth rate. The bacteria count was 784 after 2 hours and 117649 after 6 hours. What is the relative growth rate?
  6. ethic and social responsibility

    Pluripotent stem cells are__________________ (Points : 1) those cells that have the potential to be used for multiple types of tissue. those cells that have potential to be used only for one type of tissue. those cells that are generally …
  7. Science

    Actively dividing cells can be found in? meristems. xylem tissue. epidermal tissue. center of stems. phloem tissue. help
  8. Science

    Which of the following tissues would send a message to the brain indicating that someone has touched something hot?
  9. Biology (High school science)

    If non-nucleated cells of meristematic tissue are used for tissue culture, then growth rate will be : a) High b) Average c) Very low d) Growth may not take place. Please help!
  10. Calculus 2

    A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells. (a) Find a formula for the total number of cells in …

More Similar Questions