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
