Question

Stacey collects baseball cards and recently acquired the rookie cards of a pitcher and a catcher who are being inducted into the Baseball Hall of Fame. The current value of the pitcher's card is $44, and the current value of the catcher's card is $38. Each card is expected to increase in value by 3% per year. Which function can Stacey use to predict the combined value of the two cards, V(x), in x years?

Answer 1

The combined value of the two cards is
`V(x)=82(1.03)^x`.

Explanation:

The exponential growth function is defined as

`P(x)=P_0(1+r)^x`

Where, P₀ is initial value, r is growth rate and x is number of years.

The initial value of pitcher's card is $44 and the value of card is expected to increase by 3% per year. The value of pitcher's card after x years is

`F(x)=44(1+0.03)^x`

`F(x)=44(1.03)^x`

The initial value of catcher's card is $38 and the value of card is expected to increase by 3% per year. The value of catcher's card after x years is

`G(x)=38(1+0.03)^x`

`G(x)=38(1.03)^x`

The combined value of two cards is defined as

`V(x)=F(x)+G(x)`

`V(x)=44(1.03)^x+38(1.03)^x`

`V(x)=(44+38)(1.03)^x`

`V(x)=82(1.03)^x`

Therefore, the combined value of the two cards is
`V(x)=82(1.03)^x`.