the function $g(x) = 32 - 0.08x$ models the gallons of gasoline remaining in a trucks fuel tank after driving $x$ miles. after how many miles will the truck run out of fuel?

32
256
80
400

Question

the function $g(x) = 32 - 0.08x$ models the gallons of gasoline remaining in a trucks fuel tank after driving $x$ miles. after how many miles will the truck run out of fuel?

32
256
80
400

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Models", "Linear Functions" ], "new_concepts": [], "current_concepts": [ "Linear Models", "Linear Functions", "Function Evaluation" ] } ## Set the fuel function to zero $$ g(x) = 0 $$ ## Substitute the function expression $$ 32 - 0.08x = 0 $$ ## Solve for x $$ \begin{aligned} 0.08x &= 32 \ x &= \frac{32}{0.08} \ x &= 400 \end{aligned} $$

(A) 32

(B) 256

(C) 80

(D) 400

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

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QUESTION IMAGE

Question

Explanation:

Set the fuel function to zero

Substitute the function expression

Solve for x

Answer: