## jaylelile one year ago 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

1. anonymous

I am assuming the trailing x's are exponents.

2. anonymous

So you know that y must be of the form P*a^x for some a and P = $500. 3. anonymous Knowing that after 2 years, the item costs$551.25. This means that $551.25 = 500 \times a^2$

4. anonymous

Can you solve for $a$ now?

5. anonymous

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

6. anonymous

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