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?

a)exponential
b)logarithmic
c)linear
d)quadratic

Answer – C (Linear Function)
EXPLANATION

Given,
The volume of the gas is fixed
The pressure, p is related to its temperature, t as highlighted below:

When t = 44, p = 91
When t = 52, p = 93
When t = 60, p = 95
When t =68, p = 97
When t = 76, p = 99

From the above progression of values, we see that starting from 44 degrees Celsius and 91 Pascal, there is a proportionate 2 Pascal increase in pressure for every 8 degrees Celsius increase in the temperature of the gas.

Therefore, (t – 44)/8 = (p – 91)/2

Multiply both sides of the equation by 8
[(t – 44)/8] * 8 = [(p – 91)/2] * 8
t – 44 = 4(p – 91)
t – 44 = 4p – 364

Add 364 to both sides of the equation
t – 44 + 364 = 4p – 364 + 364
t + 320 = 4p
t = 4p – 320

This a linear function; f(x) = y = a + bx
Where
y is the temperature, t
x is the pressure, p
a = -320
b = 4