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!