# math

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
increasing.

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

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

## 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