12. theodore purchased a vintage painting from an art dealer worth $480. the dealer noted that the value of the painting will increase by 12 percent per year. what is the initial value of the painting?

12
0.12
480
1.12

Question

12. theodore purchased a vintage painting from an art dealer worth $480. the dealer noted that the value of the painting will increase by 12 percent per year. what is the initial value of the painting?

12
0.12
480
1.12

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth", "Growth Factor" ], "new_concepts": [], "current_concepts": [ "Exponential Growth", "Growth Factor", "Equation Modeling" ] } ## Identify the given values Using the *Exponential Growth* knowledge point $$ \begin{aligned} &\text{Purchase value} = \$480\ &\text{Annual growth rate } (r) = 12\% = 0.12 \end{aligned} $$ ## Determine the initial value Using the *Exponential Growth* and *Growth Factor* knowledge points $$ \begin{aligned} &V(t) = a(1 + r)^t\ &a = V(0) = 480 \end{aligned} $$

(A) 12

(B) 0.12

(C) 480

(D) 1.12

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Growth" ] }

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Question

Explanation:

Identify the given values

Determine the initial value

Answer: