Question

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

Answer 1

y = 500(1 + r)^x; where r is the rate and x is the number of years.
500(1 + r)^2 = 551.25
(1 + r)^2 = 551.25/500 = 1.1025
1 + r = sqrt(1.1025) = 1.05

Therefore, the equation that represents y, the value of the item after x years is
y = 500(1.05)^x