Suppose that a population of bacteria triples every hour and starts with 700 bacteria.
(a) Find an expression for the number n of bacteria after t hours.
(b) Estimate the rate of growth of the bacteria population after 1.5 hours.

Answers

Answer 1

Answer:

(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]

(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.

Step-by-step explanation:

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)=aˣ

being a real positive.

When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.

An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.

In that case, the formula used to model the growth of a population is given by:

P(t)=P0*[tex]a^{t}[/tex]

where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.

In this case:

P0=700a=3

Replacing, you get:

P(t)=700*[tex]3^{t}[/tex]

An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]

The derivative of this function P (t) is:

n'(t)=700*ln(3)*[tex]3^{t}[/tex]

and reflects the growth rate of the bacteria population.

So, the rate of growth of the bacteria population after 1.5 hours is:

n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]

Solving, you get:

n(1.5)≅ 3,996

The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.


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Answer:  B) II and III

====================================================

Explanation:

Check out the diagram below.

On the left side shows ASA can be used to prove the triangles congruent. Note the color coding to see how the angles match up. Also note that the segment TR is between angles STR and SRT. The order is important because ASA is different from AAS.

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Given two point:  (x,y) = (-6,2)

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Answers

Answer:

[tex](0,-5)[/tex]

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Alg I

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Step-by-step explanation:

Step 1: Define

Point (-4, -9)

Point (4, -1)

Step 2: Find midpoint

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Answers

Answer:

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Step-by-step explanation:

110 x 90 = 9900

90 x 10 = 900

9900 - 900 = 9000

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Answers

Answer:

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Step-by-step explanation:

Generally the null hypothesis is  rejected (that the result is significant ) when the p-value is less that the the level of significance

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Answer:

Exact form:

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Decimal Form:

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Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

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Answers

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Step-by-step explanation:

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Answers

Answer:

The probability is P(500 < X  < 700 ) =  0.60044

Step-by-step explanation:

From the question we are told that

    The mean is  [tex]\mu = 544[/tex]

     The standard deviation is  [tex]\sigma = 103[/tex]

Generally the percentage of applicant that scored between 500 and 700 is mathematically represented as

      [tex]P(500 < X < 700 ) = P(\frac{500 - 544}{103} < \frac{X - \mu }{\sigma } < \frac{700 - 544}{103} )[/tex]

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Generally from the z-table, the area under the normal curve to the left corresponding to    1.5146 and     -0.4272  is

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Answers

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Answers

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Answers

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Answers

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Answers

The question is incomplete. The complete question is :

The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. Suppose you live in a state where the environment is conducive to good health and low stress and you believe the conditions in your state promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 25 persons 65 to 74 years of age in your state.

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Chronic heart disease is a condition where a person's heart have trouble to pump blood to the body. It develops over a period of time.

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2 points
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40 words: 1 minute
100 words: 2 minutes


Answers

45. It’s just dividing 135 by 3.

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Answers

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Answers

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75*1.05 = $78.75

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gets paid 15 per hour what is the minumim number of hours that joseph must work per week to make $450 per moth? (1moth=4weeks)

Answers

Answer:

Minimum of 7 1/2 hours ( 7 hours, and 30 minutes )

Step-by-step explanation:

Rate = money / time

time = money / rate

_____________

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_____________

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