Question

A baseball card is originally worth 3$. It increases by 7% every year while the player is still active. After the player retires it increases 10% every year. If a player remains active for 7 years, how much is the baseball card worth after 20 years?

Answer 1

`\$16.64`

Explanation:

we know that

The exponential function while the player is still active is equal to

`y=3(1.07)^(x)`

where

y ----> is the value of the baseball card

x ----> the time in years

Find the value of y for x=7 years (7 years still active)

`y=3(1.07)^(7)=\$4.82`

After 20 years

x=20-7=13 years (13 years retired player)

The initial value is
`\$4.82`

The new equation is equal to

`y=\$4.82(1.1)^(x)`

substitute

x=13 years

`y=\$4.82(1.1)^(13)=\$16.64`