Math

(Growth of Cells) Suppose that after t hrs, there are p (t) cells present in a culture, where P(t) = 5000e*^2t

a) How many cells were present initially?
b) Give a differential equation satisfied by P(t)
c) When will the population double?
d) When will 20,000 cells be present?

  1. 👍
  2. 👎
  3. 👁
  1. a. "initially" means time = 0
    P(0) = 5000e^2(0) = 5000e^0 = 5000

    b. P(t) = 5000*e^(2t)

    [d/du]e^u = e^u du

    Therefore, P'(t) = 5000*2e^(2t)
    P'(t) = 10000e^(2t)

    c. Set e^(2t) = 2.
    2t = ln2
    t = (ln2)/2

    The population will double every (ln2)/2 hours.

    d. set P = 20000 and solve for t.

    20000 = 5000e^(2t)
    4 = e^(2t)
    ln4 = 2t
    2ln2 = 2t
    ln2 = t

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. biology

    Which of the following is not a principle of cell theory? a. cells are the basic units of life. b. All living things are made of cells c. Very few cells are able to reproduce*** d. all cells are produced from existing cells.

  2. science

    why would Hooke's discovery have been impossible without the invention of the microscope? A. Because all living things are made up of cells. B. Because cells are too small to see without a microscope C. Because cells are the

  3. Health

    The three lines of defense your body has against disease include all except? A. physical and chemical defenses B. inflammation C. immune system D. scarring True or false B cells and H cells are two important cells in the immune

  4. Science

    How are leaf cells and root cells different? A. Leaf cells have nuclei, but root cells do not. B. Leaf cells have chloroplasts, but root cells do not. C. Leaf cells can reproduce, but root cells cannot. D. Leaf cells can absorb

  1. Biology

    Which of the following statements is true? Since all cells carry out cellular repiration, they contain mitochondria. A cell cannot be subdivided into smaller units that maintain the living state. Plant cells contain chloroplasts

  2. Physics

    A given solar cell has the following specifications: Isc=4A Voc=0.7V 36 identical cells with the above specifications are to be interconnected to create a PV module. 1- What is the open-circuit voltage (in V) of the PV module if

  3. Science

    Which of the following is not part of the cell theory? (1 point) Cells are the building blocks of life. All living things are made up of cells. All cells are created from other cells through cell division. The nucleus is the

  4. Calculus

    A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 69 cells. (a) Find the

  1. Biology

    1. In which phase do cells rest?- Interphase. 2. Gametes (sex cells) are formed during a process called?- Meiosis. 3. In what phase of mitosis do chromosomes split into sister chromatids?- Anaphase. 4. Which type of stem cell is

  2. mathematics

    If you start a biology experiment with5000000 cells and 25% of the cells are dying every minute, how long with it be before there are fewer than 1000 cells?

  3. biology

    What is the term for cells used for reproduction that contain the haploid number of chromosomes? parent cells somatic cells zygotes gametes D

  4. Bio

    A biologist was experimenting with a corn plant that had previously incorporated radioactive carbon into starch stored in its cells. She measured the radioactivity present in the following compounds: Sugar extracted from the plant

You can view more similar questions or ask a new question.