The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years? y = 500(0.05)x y = 500(1.05)x y = 500(0.1025)x y = 500(1.1025)x

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The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years? y = 500(0.05)x y = 500(1.05)x y = 500(0.1025)x y = 500(1.1025)x

Algebra
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I am assuming the trailing x's are exponents.
So you know that y must be of the form P*a^x for some a and P = $500.
Knowing that after 2 years, the item costs $551.25. This means that \[$551.25 = $500 \times a^2\]

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Other answers:

Can you solve for \[a\] now?
\[a = \sqrt{\frac{ 551.25 }{ 500 }} = 1.05\]
Your final expression for y is: \[y = $500 \times (1.05)^x\]

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