Question

A collector's hockey card is purchased in 1990 for $5. The value increases by 6% every year. a) Write an equation that models the value of the card, given the number of years since 1990. b) Determine the increases in value of the card in the 4th year after it was purchased (from yr 3 to yr4) c) Determine the increases in value of the card in the 20th year after it was purchased.

Answer 1

You can look at the first couple years to establish a pattern. In 1991 (1 year after 1990), The worth of the card is 5*1.06.

In 1992 (2 years after 1990), the worth of the card is 5*1.06*1.06, or
\[5(1.06)^2\]
After 3 years, it's
\[5(1.06)^3\]
After n years, it's
\[5(1.06)^n\]