Part 1: Provide a mathematical justification as to why Johnny’s function cannot

Question

Part 1: Provide a mathematical justification as to why Johnny’s function cannot be used to model the relationship between the pressure and the volume in the tank. Be sure to use your knowledge of rational and quadratic functions (second differences, domain, range, asymptotes, intercepts, etc.) to answer the question. Give at least two reasons why the function representing the data is not quadratic.

Part 2: Use the information provided to determine a function that can be used to determine the pressure inside the propane gas tank based on the volume of gas that is added to the tank. Write your equation and graph the function.

Part 3: Given that the tanks can only handle a pressure of at most 240,000 psi without bursting, determine the maximum volume of compression for the gas in the tank.

Part 4: Which of the following sets of data best represents an inverse variation?

Part 5: Which equation best represents the given set of data?

Part 6: The volume of a gas in a container varies indirectly with the pressure. If the gas occupies 44 cubic centimeters of volume when the pressure reading is 5 kPa? What volume does it occupy under a pressure reading of 20 kPa?

A 11 cm3             
B 22 cm3    
C 176 cm3    
D 220 cm3    

Problem Situation The table below shows the relationship between the pressure readings in a propane tank as 10 ml of gas are compressed at various volume readings in the tank.
Volume (l) Pressure (psi) 1.5 16,000 2 12,000 2.5 9,600 3 8,000 4 6,000 5 4,800

Johnny, who took Algebra several years back, decided to use a technique he learned called quadratic regression that finds a quadratic equation to model a set of data. The quadratic equation he found is shown in the screen below on the left. He then graphed the equation, which is shown in the screen below on the right.

Part 1: Provide a mathematical justification as to why Johnny’s function cannot be used to model the relationship between the pressure and the volume in the tank. Be sure to use your knowledge of rational and quadratic functions (second differences, domain, range, asymptotes, intercepts, etc.) to answer the question. Give at least two reasons why the function representing the data is not quadratic.

Part 2: Use the information provided to determine a function that can be used to determine the pressure inside the propane gas tank based on the volume of gas that is added to the tank. Write your equation and graph the function.

Part 3: Given that the tanks can only handle a pressure of at most 240,000 psi without bursting, determine the maximum volume of compression for the gas in the tank.

Part 4: Which of the following sets of data best represents an inverse variation?

A x y 1 7.2 2 5 3 3.2 4 1.8 5 2 6 .2     C x y 2 5 4 4 6 3 8 2 10 1     B x y 1 16 2 8 3 4 4 2 5 1     D x y 2 57 3 38 6 19 19 6 38 3             

Explanation / Answer

part 5

everytime if we multiply x with y we get a constant value 24

that is xy = 24

from each relationship y = 24/x describes the given data ( option d)

part 6

The volume of a gas in a container varies indirectly with the pressure

let volume = V

pressure = P

V = k/ P

where k is proportionality constant

gas occupies 44 cubic centimeters of volume when the pressure reading is 5 kPa

44 = k * 5

k = 44/5

volume when pressure = 20kPa

V = 44/5 * 20 = 176 cubic centimetres ( option c)

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