In a group of four, work through the following. You will need a metric tape or meterstic...

In a group of four, work through the following. You will need a metric tape or meterstick.

a. Place your math book on a desk and measure the distance (to the nearest centimeter) from the floor to the top of the book. Record the distance.

b. Place a second math book on top of the first and measure the distance (to the nearest centimeter) from the floor to the top of the second book. Record the distance,

c. Continue this procedure for all four of Your math books and complete the following table and graph:

d. Without measuring, what is the distance from the floor with 0 books? 5 books?

e. Write a rule or function for d(x), where d(x) is the distance above the floor to the top of the stack of books and x is the number of books.

f. Suppose the distance from the floor to the ceiling is 2.5 m. If you stack the books as described above, how many books would be needed to reach the ceiling?

g. The function h(x) = 34x + 70 represents the height of another stack of x math books (in centimeters) of the same thickness on a cabinet. What does the function tell you about the height of the cabinet?

h. Suppose that a table with a stack of similar math books (more than 10) is 200 cm high. If the top math book is removed, the height is 197 cm. If a second book is removed, the height is 194 cm. What is the height if 5 books are removed?

i. Write a function h(x) for the height of the stack in part (h) after x books are removed.