the general equation for depreciation is given by $y = a(1 - r)^t$, where $y =$ current value, $a =$ original cost, $r =$ rate of depreciation, and $t =$ time, in years.

the original value of a car is \$24,000. it depreciates 15% annually. what is its value in 4 years?

Question

the general equation for depreciation is given by $y = a(1 - r)^t$, where $y =$ current value, $a =$ original cost, $r =$ rate of depreciation, and $t =$ time, in years.

the original value of a car is \$24,000. it depreciates 15% annually. what is its value in 4 years?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Decay Modeling" ], "new_concepts": [], "current_concepts": [ "Exponential Decay Modeling" ] } ## Identify the given parameters Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} A &= 24000 \ r &= 0.15 \ t &= 4 \end{aligned} $$ ## Substitute values into the formula Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} y &= 24000 \times (1 - 0.15)^4 \ y &= 24000 \times (0.85)^4 \end{aligned} $$ ## Calculate the final value Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} (0.85)^4 &= 0.52200625 \ y &= 24000 \times 0.52200625 \ y &= 12528.15 \end{aligned} $$ The general equation for depreciation is given by $y = A(1 - r)^t$, where $y =$ current value, $A =$ original cost, $r =$ rate of depreciation, and $t =$ time, in years. The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years? $12,528.15 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Decay Modeling" ] }

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Question

Explanation:

Identify the given parameters

Substitute values into the formula

Calculate the final value

Answer: