a new car sells for $25,000. the value of the car decreases by 15% each year. what is the approximate value of the car 5 years after it is purchased?

$25,000(1-0.15)^5$, or approximately $11,093
$25,000-1500(5)$, or approximately $17,500
$25,000(0.15)^5$, or approximately $18,984
$25,000-(100-15)(5)$, or approximately $24,575

Question

a new car sells for $25,000. the value of the car decreases by 15% each year. what is the approximate value of the car 5 years after it is purchased?

$25,000(1-0.15)^5$, or approximately $11,093
$25,000-1500(5)$, or approximately $17,500
$25,000(0.15)^5$, or approximately $18,984
$25,000-(100-15)(5)$, or approximately $24,575

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Growth", "Exponential Modeling" ], "new_concepts": [ "Exponential Decay" ], "current_concepts": [ "Exponential Decay", "Exponential Modeling" ] } ## Set up the exponential decay model $$ \begin{aligned} &P = 25000\ &r = 0.15\ &t = 5\ &V(t) = P(1 - r)^t \end{aligned} $$ ## Substitute the given values $$ \begin{aligned} &V(5) = 25000(1 - 0.15)^5\ &V(5) = 25000(0.85)^5 \end{aligned} $$ ## Calculate the approximate value $$ \begin{aligned} &25000(0.85)^5 \approx 11093.02\ &\text{Value} \approx \$11,093 \end{aligned} $$

(A) $25,000(1-0.15)^5$, or approximately \$11,093

(B) $25,000-1500(5)$, or approximately \$17,500

(C) $25,000(0.15)^5$, or approximately \$18,984

(D) $25,000-[(100-15)(5)]$, or approximately \$24,575

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

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QUESTION IMAGE

Question

Explanation:

Set up the exponential decay model

Substitute the given values

Calculate the approximate value

Answer: