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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Functions", "First Differences" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "First Differences", "Function Modeling" ] } ## Calculate differences in temperature $$ \begin{aligned} \Delta T_1 &= 52 - 44 = 8 \ \Delta T_2 &= 60 - 52 = 8 \ \Delta T_3 &= 68 - 60 = 8 \ \Delta T_4 &= 76 - 68 = 8 \end{aligned} $$ ## Calculate differences in pressure $$ \begin{aligned} \Delta P_1 &= 93 - 91 = 2 \ \Delta P_2 &= 95 - 93 = 2 \ \Delta P_3 &= 97 - 95 = 2 \ \Delta P_4 &= 99 - 97 = 2 \end{aligned} $$ ## Determine the constant rate of change $$ \frac{\Delta P}{\Delta T} = \frac{2}{8} = 0.25 $$

exponential

logarithmic

linear

quadratic

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate differences in temperature

Calculate differences in pressure

Determine the constant rate of change

Answer: