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

Question

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

anonymous · Answer

I am assuming the trailing x's are exponents.

anonymous · Answer

So you know that y must be of the form P*a^x for some a and P = $500.

anonymous · Answer

Knowing that after 2 years, the item costs $551.25. This means that $$$551.25 = $500 \times a^2$$

anonymous · Answer

Can you solve for $$a$$ now?

anonymous · Answer

$$a = \sqrt{\frac{ 551.25 }{ 500 }} = 1.05$$

anonymous · Answer

Your final expression for y is: $$y = $500 \times (1.05)^x$$