Question

the pressure of a fixed volume of a certain gas is related to its temperature as shown in the table below.

temperature of gas vs. pressure
temperature (in degrees celsius) | pressure (in pascals)
44 | 91
52 | 93
60 | 95
68 | 97
76 | 99

which type of function best models the data in the table?

exponential
logarithmic
linear
quadratic

Explanation:

Calculate first differences of the independent variable

$$ \Delta T = 52 - 44 = 8,\quad 60 - 52 = 8,\quad 68 - 60 = 8,\quad 76 - 68 = 8 $$

Calculate first differences of the dependent variable

$$ \Delta P = 93 - 91 = 2,\quad 95 - 93 = 2,\quad 97 - 95 = 2,\quad 99 - 97 = 2 $$

Determine the constant rate of change and model type

$$ \frac{\Delta P}{\Delta T} = \frac{2}{8} = 0.25 \text{ pascals/}^\circ\text{C} $$

Answer:

• exponential
• logarithmic
• linear (Correct answer)
• quadratic