Katrina is studying the effect of foreign substances on bacteria populations. If she introduces a
beneficial substance, such as food, the bacteria population grows. If she introduces a harmful substance,
such as a poison, the bacteria population decreases. The function
f(x) = x4 - 20x3 + 141x2 - 414x+ 432, where x is the time in days, models the bacteria population rate of growth or decrease over time. Determine when the bacteria's population was

b) Describe the bacteria population between days 3 and 6. Explain what positive, negative, and values of 0
mean in this situation.

asked by Eric
  1. f(x) increasing when f'(x) > 0
    f'(x) = 4x^3 - 60x^2 + 282x - 414
    = 2(x-3)(2x^2-24x+69)
    The roots are 3,6±√(3/2) = 3.00,4.78,7.22
    So, f' > 0 in (3,6-√(3/2) U (6+√(3/2),∞)

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. science

    g) Use the substances given in table 1 to calculate the volume of 270 g of aluminum. The densities of substances given: glycerol (substance a) = 0.97 g/mL isoprop (substance b) = 1.20 g/mL water (substance c) = 0.85 g/mL How would
  2. Science

    A vaccine can protect you against a disease because it (1)destroys toxic substances from bacteria before they can make you sick\ (2) stimulates your immune system against the pathogens (3) kills any pathogenic bacteria in your
  3. Chemistry

    Assume that a reaction occurs in which unknown substances R and S react to form unknown substances T and U. From the information below, determine the mass of substance T that will be formed if 45.0 grams of substance R reacts with
  4. Chemistry

    Consider the densities of the liquid substances listed. a) How will substance X, a solid, with density of 0.87 g/cm^3, behave when placed in each of the other pure liquids? b) Sketch and label a test tube containing substances
  5. science help ASAP please

    1. Angiosperms have organs such as ______________ and produce seeds. The are described as _________________plants. (1 point) flowers; vascular stems; pollinated rhizoids; vascular leaves; non-vascular 4. Of the following, which is
  6. Math Word Problem

    At 6am a few bacteria fall into a can of syrup in a broken garbage bag. The conditions of warmth, moisture, and food are perfect for growth and the population doubles every 20 minutes. By 6pm the bacteria are overcrowded and dry
  7. English

    Choose the best answer 1. What do you get if you mix common bacteria and vinegar. The word common means a. multiple b. ordinary - the answer c. lower-class d. poisonous 2. It is a serious question. The answer is you get bacteria
  8. Chemistry

    Substances A and B, initially at different temperatures, come in contact with each other and reach thermal equilibrium. The mass of substance A is twice the mass of substance B. The specifi c heat capacity of substance B is twice
  9. Math (Quadractic function)

    Hi can you help me find the solution for this one? I have the answers at the end but I want to study how did it end with that. Thanks :) The number N of bacteria in a refrigerated food is given by N(T) = 10T^2 - 20T + 600, 1
  10. science HElp

    Ph scale Which on is true A substance with ph is twice as acidic as substance with ph of 4. A subtances with ph 3 is 10 as acidic as substance with ph of 4. A substance with ph 3 twice as alkies as substances with ph 4. a

More Similar Questions