Question

You purchased a baseball card for $8 when you were 10 years old. The value of the card increased by 5% each year. Write an exponential model that gives the value y (in dollars) of the card t years after you purchased it.

Answer 1

This is exponential growth which can always be expressed as:

f=ir^t, f=final value, i=initial value, r=rate, t=time, in this case:

f=8((100+5)/100)^t

f=8(1.05^t)

Answer 2

The exponential function that represents the value of the baseball card is y = $8(1.05^t).

What is the exponential function that represents the value of the baseball card?

An exponential function is usually in the form: y = m^x. When the value of the baseball increases, it means that it is appreciating with the passage of time.

The formula that can be used to represent appreciation is:

FV = P (1 + r)^n

• FV = Future value
• P = Present value
• R = rate of increase
• N = number of years

y = $8(1.05)^t

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