Problem 1: Children’s Growth

 

 

 

 A study of the data representing the approximate average heights of children from birth to 12

 

 

 

 years (144 months) has shown the following two equations. hg The function is the radical

 

 

 

 function representing the girls’ heights in inches after x months, and the function hb

 

 is the radical

 

 

 

 function representing the boys’ heights in inches after x months (0< x<  144 months).

 

Y=hg (x)= 3.08 √x +18.97

 

Y=hb(x)=2.87 √x +20.08

 

 

 

 

 

1. Choose five different values of x between 0 and 144 months, and calculate the values of each of

 

 

 

 

 

these functions for the chosen x values. Show all of your work and display these calculated values

 

 

 

of y= hg (x) and y=hb(x) in “t-tables” in the Answer Form supplied.

 

2.

 

 

 

2. Use these five different values of x and the corresponding calculated values of both functions, together with Excel or another graphing utility, to draw the graphs of these two functions. These graphs should be drawn on the same coordinate system so that the two functions can be easily compared. Insert those graphs into the Answer Form.

 

 

 

 

 

3. Set the two functions equal to each other, and solve the resulting radical equation for x. This value of x will be the age in months when boys and girls are the same height. (Show all of the steps for solving this radical equation on the Answer Form provided.)

 

 

 

 

 

4. What is the height in inches when boys and girls (according to these radical functions) are the same height? (Show all of your work on the Answer Form provided.)

 

 

 

 

 

5. Based on each of the two radical functions above, what is the average change in height per month for girls and the average change in height per month for boys between the two values of

 

 

 

 

 

x (x = 30 months and x = 60 months)? (Show all of your work on the Answer Form provided.)

 

 

 

6. Describe the transformations of the radical function f(x ) √x that will result in each of these

 

 

 

functions.

 

 

 

 

 

7. Which intellipath Learning Nodes helped you with this problem?

 

 

 

 

 

Problem 2: Average Cost

 

Your company is making a product item. The fixed costs for making this product are b, and the variable costs are mx, where x is the number of items produced. The cost function is the following linear function:

 

C(x)=mx+b

 

The average cost is the total costs divided by the number of items produced, which is a rational function,

 

as follows:

 

-/c=mx+b/x=m+bx  x>/_1

 

 

 

-=mx+b=m+ b           x> 1

 

C    x              x      (the c belongs under the first -,and x belongs under the mx+b, the x belongs under the b

 

 

 

1. Based on the first letter of your last name, choose values for m and b from the following tables (Neither m nor b has to be a whole number):

 

 

 

First letter of your last name	Possible values for m
A–F	$10–$19
G–L	$20–$29
M–R	$30–$39
S–Z	$40–$49

 

 

 

The first letter of my last name :K     Possible values for m:$20-$29

 

 

 

First letter of your last name	Possible values for b
A–F	$100–$149
G–L	$150–$199
M–R	$200–$299
S–Z	$300–$399

 

 

 

The first letter of my last name :K     Possible values for b: $150–$199

 

 

 

2. Make up the type of company and a product that you think fits the values of m and b that you have chosen in Question 1, and briefly describe the company and product. (There is no wrong

 

 

 

 

 

answer except to not answer the question. Be creative in developing your scenario, but do not overdo it.)

 

 

 

3. Important: By Wednesday night at midnight, submit in a Word document only your name and your chosen values for m and b. Submit this in the Unit 4 submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes.

 

 

 

4. Choose five values of x < 50, and calculate the corresponding values of  line over the C(x).

 

Display these x and line over the C(x) values in a t-table. (Show all of your work details for these calculations. Please review this we site:purple math to see how to type mathematics using the keyboard symbols.)

 

 

 

 

 

 

 

5. Using Excel or another graphing utility, draw the graph of your average cost function, as follows:

 

-/c=mx+b/x=m+bx  x>/_1

 

 

 

 -=mx+b=m+ b           x> 1

 

C    x              x      (the c belongs under the first -,and x belongs under the mx+b, the x belongs under the b

 

 

 

6. What happens to your average cost rational function when x gets very large? Explain your answer.

 

 

 

7. How many items must be produced before the average cost is 1.5 times your chosen value of m? (Show all of your work.)

 

 

 

8. Describe the transformations of the rational function f(x ) =1xthat will result in your average

 

 

 

cost function. (Hint: What transformation types are used to get from f(x ) =1/x to g(x)=m+b/x=m+b(1x)?)

 

 

 

9. Does your average cost function have a horizontal asymptote? If so, what is that horizontal asymptote equation? (Explain your answer.)

 

10. Which intellipath Learning Nodes helped you with this problem?

 

Reference

 

Formatting math as text. (n.d.). Retrieved from the Purple Math Web site: http://www.purplemath.com/modules/mathtext.htm