Question

Part 2: Solve a real-world problem using a square root function.

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.
The total length of each row of bookshelves will be 45 of the length of the storage space.
Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)

Write a function that expresses f(x). (10 points)



Graph the function. (10 points)

Answer 1

To find the length of a row of bookshelves, we first need to find the length of one side of the square space that Isabel rents, since all spaces must be square. We can do this by taking the square root of the area of the space that Isabel rents:

Side length of square space = √(x)

Then, we can use the fact that the total length of each row of bookshelves will be 45 times the side length of the square space, so we can write:

f(x) = 45√(x)

To graph this function, we can plot f(x) on the y-axis and x on the x-axis, since f(x) is a function of x. We can use a graphing calculator or software to plot the graph, or we can use a table of values to plot the graph by hand. Here is a table of values for f(x) for x ranging from 100 to 8100, in increments of 100:

(hopefully u can understand my "graph")

x f(x)

100 67.08

200 94.87

300 115.47

400 133.15

500 149.16

600 163.66

700 177.00

800 189.31

900 200.75

1000 211.43

1100 221.46

1200 230.91

1300 239.86

1400 248.34

1500 256.41

1600 264.10

1700 271.45

1800 278.48

1900 285.22

2000 291.68

2100 297.89

2200 303.85

2300 309.58

2400 315.09

2500 320.39

2600 325.48

2700 330.38

2800 335.10

2900 339.64

3000 344.01

3100 348.21

3200 352.24

3300 356.11

3400 359.82

3500 363.37

3600 366.76

3700 370.00

3800 373.09

3900 376.03

4000 378.82

4100 381.47

4200 384.00

4300 386.39

4400 388.65

4500 390.79

4600 392.81

4700 394.71

4800 396.49

4900 398.16

5000 399.71

5100 401.15

5200 402.48

5300 403.70

5400 404.81

5500 405