the value of a collectors item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years.

$578.81
$607.75
$1687.50
$2531.25

Question

the value of a collectors item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years.

$578.81
$607.75
$1687.50
$2531.25

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Functions", "Exponential Growth" ], "new_concepts": [], "current_concepts": [ "Exponential Functions", "Exponential Growth" ] } ## Set up the exponential growth model $$ \begin{aligned} P &= 500 \ r &= 0.05 \ t &= 4 \ A(t) &= P(1 + r)^t \end{aligned} $$ ## Calculate the value after 4 years $$ \begin{aligned} A(4) &= 500(1 + 0.05)^4 \ &= 500(1.05)^4 \ &\approx 500(1.21550625) \ &= 607.753125 \end{aligned} $$ ## Round to the nearest cent $$ A(4) \approx \$607.75 $$

(A) \$578.81

(B) \$607.75

(C) \$1687.50

(D) \$2531.25

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

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QUESTION IMAGE

Question

Explanation:

Set up the exponential growth model

Calculate the value after 4 years

Round to the nearest cent

Answer: