Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Radical Functions - help  pls!?

See attached photo first -

• The function to model the body surface area of a patient who is 68 inches tall. (

• The graph of the function.

• An interpretation of the domain/range, intercepts, and increase/decrease of the graph in terms of the problem situation.

• The body surface area of the patient with work shown.

• The weight of the patient with work shown.

• The dosage of the medicine with work shown. Relevance

1: the function to model the surface area would just be B(W) = sqrt(68*W/3131)

2: When you graph it, the function will go through (0,0), and it will cross 2 at 184.17 pounds.

3: The domain is the weight of the individual in pounds, so it must be positive. The range of the function is the total body surface area. The increase in weight will be a growth curve with a slowing rate of growth with increasing marginal weight addition.

4: B(W) = sqrt(68*161/3131)=sqrt(3.4966)=1.87 m^2

5: 1.98 m^2 = sqrt(68*W/3131)3.9204 = 68*W/3131W=180.5 lbs

6: B(W) = sqrt(68*201/3131)=sqrt(4.3654)=2.09 m^2

dosage = 15 mg/m^2 * 2.09 m^2 = 31.34 mg

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• 1. B(W)=√(68W/3131)

3. Domain [0,∞)    ;  Range [0,∞)

4. From graph B(161) = 1.87 m²

From algebraic calculations

B(161)=√((68*161)/3131) = 1.87 m²

5. 1.98 = √(68W/3131)

1.98² = 68W/3131

W = 1.98² * 3131/68 = 180.5 lbs

6. B(201)=√(68*201/3131) = 2.09 m²

Dosage = (15 mg/m²)(2.09 m²) = 31.35 mg • Log in to reply to the answers
• 1.   B = sqrt[ (HW/3131)

B = sqrt[ (68W/3131)

that's it  ..  B(W) does not mean a product B X W ..  this is function notation  ...  B(W) is read .. B is a function of W ... meaning that the formula to the right of the equal sign will ONLY have W as a variable

2.  the directions .. use technology -- means USE some graphing calculator --  most use a TI something...

3. .  look at the graph

4.  w = 161  <<<  use in a calculator

B = sqrt[ (68W/3131)

B = sqrt[ (68*161/3131) = 1.87 sq meters

5.  B = 1.98

1.98 = sqrt[ (68W/3131)

3.9204  = 68W/3131

W  =  180.51 pounds

6.  TWO steps

B = sqrt[ (HW/3131)

B = sqrt[ (201*68/3131)  = 2.0893 m^2

dosage  =  15 X 2.0893  =  31.34 mg

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• [ this is a corrected version -- the operator that looks like a minus on my screen, could be a multiplication sign ]

You are given a function (called "B") where the variables used are H and W.

Then you are given one of the values and it becomes "fixed" in the function, leaving only "W" as the variable value (the weight in pounds).

It could also have been written as

B(H, W) = √[ (H * W) / 3131 ]

to show that the value called B, depends on the input value used for two variable: H and W.

The function, for patients that are 68 inches tall, is now

B(W) = √[ (68*W) / 3131 ]

You could, if you wanted to, find the fraction for 68/3131, then find the square root of that in order to pull that number out of the radical:

B(W) = √( 0.0217183*W)

B(W) = 0.1473713*√W

All three versions are OK (and should lead to the same answer when given a value for W)

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To graph this, simply use different values for W, and plot the values on the graph.

For example, if the weight is 121 pounds, then

W = 121

√W = 11

B(121) = 0.1473713 * 11 = 1.621 m^2

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I do not understand what is asked in number 3.

DOMAIN = the set of values that can be used for W and for which the function will give a "well-defined" answer.

RANGE = the set of values that can be hit by B(W) once you have tried all the values for W.

One thing that is clear is that neither the domain (weight of patient) nor the range (skin area) can be zero or negative.

If you find such a formula in a scientific paper, the article would give the domain over which the formula can be trusted.

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4)

repeat the same operation as above (use the formula) except you use

W = 161 (instead of my example of 121)

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5)

You are aksed to use the formula "backwards": they give you the area (the value of B(W) ) and they ask you to find the weight.

B(W) = √[ (68*W) / 3131 ]

they give you B(W) = 1.98

1.98 = √[ (68*W) / 3131 ]

square both sides (squaring a square root... they cancel each other)

3.92 = (68*W) / 3131

3131 * 3.92 = 68 W

3131 * 3.92 / 68 = W

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6) The dosage is given for each square metre of skin area.

Just calculate the skin area using the formula

You are looking for B(201)

which means you are looking for B(W) when W=201

Once you find the number of square metres (the value of B(201)), you simply multiply that by the dosage.

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