Question

The value of a baseball player's rookie card began to increase once the player retired. When he retired in 2000 his card was worth $6.44. The value has increased by $2.62 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 2010?

Answer 1

The relationship between the value of the card and the number of years in retirement is expressed by the equation y = $6.44 + $2.62x.

The relationship is proportional, and the value of the card in 2010 was $32.64.

Step-by-step explanation:

To express the relationship, we can use the equation:

y = $6.44 + $2.62x

This equation represents the value of the card (y) in dollars based on the number of years the player has been in retirement (x).

The initial value of the card is $6.44, and for each year in retirement, the value increases by $2.62.

The relationship between x and y is proportional because the increase in the value of the card is consistent and predictable.

The value increases by the same amount ($2.62) each year, indicating a proportional relationship.

To find the value of the card in 2010, we can substitute x = 2010 - 2000 = 10 into the equation:

y = $6.44 + $2.62 * 10

= $6.44 + $26.20

= $32.64

The value of the card in 2010 was $32.64.