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

Answer: $244.55

Step-by-step 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.

Answer 2

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