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? a. y = 500(0.05)x b.y = 500(1.05)x c. y = 500(0.1025)x d. y = 500(1.1025)x
An exponential increase may be represented as y = A(B^x).
You can find the parameters A and B using the initial condition and the value after 2 years.
1) Initial condition: x = 0 => y = 500 => 500 = A(B^0) = A(1) = A => A = 500 => y = 500 (B^x)
2) After 2 years y = 500 (B^2) = 551.25 => (B^2) = 551.25 / 500 = 1.1025 => x = sqrt(1.1025) = 1.05.
Then A = 500 and B = 1.05 => x = 500 (1.05)^x.
Answer: option b., y = 500 (1.05)^x
