Question

Challenge The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1996 his card was worth $9.17. The value has increased by $1.65 each year since then, Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006? Express the relationship with an equation. y=?

Answer 1

$151.31. Not proportional.

y= 9.17 +1.65x

1) Gathering the data

1996 Retired $ 9.17

9.17(1.65)^x

2) Since the value of that card has been increasing 1.65 yearly, then we can write the following equation:

$y=9.17+1.65x$

For y= Value, and x =years

Let's find out the value of the card in 2006, i.e. 10 years later. Plug x=10 into the above function:

$\begin{gathered} y=9.17+1.65x \\ y=9.17+1.65(10) \\ y=9.17+16.5 \\ y=151.305\approx y=151.31 \end{gathered}$

3) Hence, the value of the card in 2006 is $151.31

(rounded off to the nearest hundredth)

And since the initial value is $9.17, then it is not a proportional relationship since an initial value of a proportional is always 0.