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. 👍 0
  2. 👎 0
  3. 👁 280
asked by Mitch
  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. 👍 0
    2. 👎 0
    posted by Marth
  2. Y e e t

    1. 👍 0
    2. 👎 0
    posted by Deez

Respond to this Question

First Name

Your Response

Similar Questions

  1. science

    what are cells made from? Please, what kind of cells? There are many kinds. Jail cells, hive cells, plant cells, animal cells, blood cells, brain cells. We need a more definitve question.

    asked by simrandeep on April 18, 2007
  2. biology

    All of the cells are in the very early stages of embryonic development and have not begun to differentiate into specialized types of cells. What type of cells would these be? A) gametes B) stem cells C) somatic cells D) epidermal

    asked by Angelina on December 6, 2016
  3. 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.

    asked by Anonymous on August 22, 2018
  4. biology

    which of the following types of cells need to make energy to perform basic functions like growing, moving, and reproducing? -animal cells -animal cells and bacteria cells -animal cells, bacteria cells, and plant cells -plant cells

    asked by please help on November 3, 2014
  5. Intro to psychology / science

    Learning and memory researchers have discovered that : A.) physical exercise promotes new cell growth, while mental ecercise only maintains exsisitng cells. B.)stem cells can divide and mature throughout adulthood. C.) age is the

    asked by pateyn on January 5, 2012
  6. Calc

    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 59 cells. (The

    asked by Joe on November 8, 2009
  7. 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

    asked by Anonymous on May 11, 2018
  8. chemistry

    4)You count your cells and have 8x10ᶺ5 viable cells/ml you want to see (dilute the cells) to end up with 2x10ᶺ5 viable cells/ml. What volume of cells will you put into 20 ml?

    asked by Daniel on December 6, 2011
  9. Biology

    4)You count your cells and have 8x10ᶺ5 viable cells/ml you want to see (dilute the cells) to end up with 2x10ᶺ5 viable cells/ml. What volume of cells will you put into 20 ml?

    asked by Daniel on December 6, 2011
  10. Advanced Biology

    The cells of cellular slime molds bear a resemblance to: a) flagellated cells b) diatoms c) ciliated cells d) dinoflagllates e) amoeboid cells I think it's b!

    asked by Jennifer on January 8, 2010

More Similar Questions