For this Applied Knowledge Assessment, you will develop your understanding of inverse equations through exploring safety issues related to scuba diving.

Scuba

This assessment is worth 75 points. Show all of your work on this sheet and submit one document.

Introduction

Scuba diving helps marine scientists explore the underwater frontier. It is also a popular sport. To dive safely, divers must understand that water pressure at depths of 30 or 40 feet can be very dangerous.
In this assessment, you will use mathematics to explore safety issues related to scuba diving. Modern scuba diving equipment allows divers to stay underwater for long periods of time, but the depth and length of dives are limited by the amount of pressure that the human body can tolerate.

Warm Up

1)Answer the following questions about inverse variation.

a)Write an equation that models the expression wherey varies inversely with x.

b)If y = 20 when x =4, solve for k.

c)Rewrite your equation from part a., subbing in the value for k that you solved for in part b.

Activity 1: Graphing


2)Write an equation that represents Boyle’s law (the volume of air varies inversely with the pressure).Use k for the variation constant.
3)Solve for k utilizing the fact that you have 4 quarts of air in your lungs when the pressure is 3 atm and 6 quarts of air in your lungs when the pressure is 2 atm.Rewrite your inverse variation equation from Question #2 using your new value for k.

4) Using your equation from Question #3, construct a table relating the volume of air in your lungs to the pressure.The values for the pressures are 1 atm, 2 atm, and 3 atm.

5)Write an equation relating volume to depth.(Hint: Replace P in your equation from Question #3 with an expression in terms of d.You do not need to simplify your equation.)

6)Using your new equation, make a table to show how the volume of air in your lungs varies with the depth.Set up your table as you would an x/y chart.Let d, the depth, be the independent variable and V, the volume, be the dependent variable.Use these values for d: 99, 66, 33, and 0 (you would be at the water’s surface when d = 0).

7)Graph the data from your chart above.Use reasonable units for d and remember to make d the x-axis.

Activity 2: Writing

In Activity 1, you found that the volume of air in a diver's lungs could more than double as the diver resurfaces. This expansion can cause the membranes of the lungs to rupture. Divers must learn to exhale properly while ascending.

8)Write an explanation of why a beginning diver is told not to hold his breath. Refer to your tables and graphs.

Activity 3: Solving

The rate at which a scuba diver uses air in the tank depends on many factors, such as the diver's age and lung capacity. Another important factor is the depth of the dive. A scuba diver continues to breathe normally while descending. Every time the diver inhales, the tank delivers enough air to inflate the diver's lungs. This means that the amount of air delivered by the tank must increase with the depth in order to withstand the increasing pressure. At greater depths, the diver uses the air in the tank more quickly. The amount of time the air will last is inversely proportional to the pressure at the depth of the dive.

9) The amount of time (t) the air will last is inversely proportional to the pressure (P) at its depth.

a) Write an inverse variation that models the relationship between tand P.

b) Suppose a tank has enough air to last 60 minutes at the surface. The pressure is 1 atm at the surface. Solvefor k.

c) The pressure is 4 atm at a depth of 99 ft. How long will it last at a pressure of 4 atm?

10)Create a table showing how long the air will last at 0 ft, 33 ft, 66 ft, and 99 ft.Construct your table to include three columns.The first column should be the depth in feet, the second the pressure in atm, the third the time in minutes.

Directions for Inserting an Image into a Word Document:

  1. Scan your document(s) and save it (them) as a .jpg file. Save the images using file names that relate to the assignment.
  1. Open the Word document.
  1. Type the following on the first line of the Word document.

“Last Name_First Name_Assignment Name”

(Example: Doe_Jane_U1L1_AKA)

  1. Save the file with a file name such as “Last Name_First Name_Assignment Name.”
  1. Place your cursor in the Word file where you want to insert the image.
  1. Select the Insert option from the top tab.

  1. Select “Picture.”
  1. Locate the file on your desktop. Click on the file and click “Insert.” The image will then be inserted into your document.

  1. The image will now be inserted into your file. It will look something like this:

Doe_Jane_U1L1_AKA

*Note: To insert another image, simply place the cursor at the end of the image and press “Enter.” You are now ready to repeat the process until you have loaded all of your images for the assignment into one Word document!