the distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table below.

stopping distance of a car vs. speed
stopping distance, d (in feet) | speed, s (in miles per hour)
20 | 17.89
40 | 25.30
60 | 30.98
80 | 35.78
100 | 40.00

which equation best represents the data in the table?

$s = 4\sqrt{d}$
$s = 0.37d + 20$
$s = 13.7\log(d)$
$s = \frac{1}{25}d^2$

Question

the distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table below.

stopping distance of a car vs. speed
stopping distance, d (in feet) | speed, s (in miles per hour)
20 | 17.89
40 | 25.30
60 | 30.98
80 | 35.78
100 | 40.00

which equation best represents the data in the table?

$s = 4\sqrt{d}$
$s = 0.37d + 20$
$s = 13.7\log(d)$
$s = \frac{1}{25}d^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation" ], "new_concepts": [ "Radical Modeling" ], "current_concepts": [ "Function Evaluation", "Radical Modeling" ] } ## Evaluate the equations at a sample data point $$ \begin{aligned} &\text{Let } d = 100 \text{ and the corresponding speed } s = 40.00.\ &\text{Option 1: } s = 4\sqrt{100} = 4 \times 10 = 40\ &\text{Option 2: } s = 0.37(100) + 20 = 57\ &\text{Option 3: } s = 13.7\log(100) = 13.7 \times 2 = 27.4\ &\text{Option 4: } s = \frac{1}{25}(100)^2 = 400 \end{aligned} $$ ## Verify the selected model with another data point $$ \begin{aligned} &\text{Let } d = 60 \text{ and the corresponding speed } s = 30.98.\ &s = 4\sqrt{60} \approx 4 \times 7.746 = 30.984 \end{aligned} $$

(A) $s = 4\sqrt{d}$

(B) $s = 0.37d + 20$

(C) $s = 13.7\log(d)$

(D) $s = \frac{1}{25}d^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the equations at a sample data point

Verify the selected model with another data point

Answer: