### Home > CALC > Chapter 6 > Lesson 6.4.2 > Problem 6-140

WHAT A CARD!

The value,

*V*, of a Honus Wagner baseball card in mint condition appreciates at 12% per year. It was sold at auction in 1991 for $461,000. If*t*= time in years since 1991, then*V*= 461000(1.12). Homework Help ✎^{t}

What was its value in 2000?

Find the average value of the card over the period 1991 - 2000.

When was the card worth the value you found in part (b)?

We are given a value function, *V*(*t*). Notice that *t* = years since 1991. Evaluate for the year 2000.

Value = *V*(*t*) = 461,100(1.12)^{t}

Examine the equation above:

What is the annual interest rate?

What is the initial value of the card?

Unlike average value (AROC), actual value (IROC) must be found with a derivative.

Let *V* '(*t*) = your answer in part (b).

The card was worth its average value in 1995 or 1996.