The value of a collectors item is expected to increase exponentially each year. The item is purchased for $500. After two years, the item is worth $551.25. Which equation represents y, the value of the item after x years?

Hi there

First we need to find the rate of increases

551.25=500 (1+r) ^2

Solve for r

First divide each side by 500 to get

551.25/500 = (1+r) ^2

And take the square root for both sides to get

(551.25/500) ^ (1/2) = 1+r

(Note that the square root is the same as the power of 1/2)

After that subtract each side by - 1 to get

R = (551.25:500) ^ (1:2) - 1

R=0.05

Since we have the rate of increases the formula is

Y=500 (1+0.05) ^x

Y=500 (1.05) ^x ... answer

Good luck!