Question

Zhang thinks that the value of a baseball card can be modeled by exponential decay and that the value will decrease at a rate of 0.2% each year. The card was originally valued at $250 in 2007. What would Zhang expect the card to be in 2018? Round the value of the card to the nearest cent. Show all work

Answer 1

The correct answer would be
$249.45
2018 - 2007 = 11
11 x 0.2% = 0.22%
0.22% of 250 = 0.55
250 - 0.55 = 249.45
$249.45

Answer 2

Answer: $244.55

Explanation:

We know that the exponential decay function is given by :-

`f(t)=A(1-r)^t` , where r is the rate of decay ( in decimal ) , A is the initial amount and t is time period.

Given : A = $250 ; r=0.002 t= 11 [From 2007 to 2018 , t=2018-2007]

Then, the expected value of card in 2018 :-

`f(11)=250(1-0.002)^(11)\\\\\Rightarrow\ f(11)=250(0.978218685265)\\\\\Rightarrow\ f(11)=244.554671316\approx244.55`

Hence,Zhang expect the card to be $244.55 in 2018.