SOLUTION: The equation V=12(1.25)^t describes the value (V) of a hockey card t years after purchase. a) What was the initial value of the hockey card? b) What was tha rate of appreciation

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: The equation V=12(1.25)^t describes the value (V) of a hockey card t years after purchase. a) What was the initial value of the hockey card? b) What was tha rate of appreciation       Log On


   

Question 119095: The equation V=12(1.25)^t describes the value (V) of a hockey card t years after purchase.
a) What was the initial value of the hockey card?
b) What was tha rate of appreciation expressed as a percentage?
c) What will be the cards value 5 years after it was purchased?
d) Use the graphing calculator to determine the number of years it would take for the card to be worth $71.53.
For (a) I got $12 , for (b) I got 25% but I am not sure. Can someone please explain this to me. Thanks:)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
V=12%281.25%29%5Et
a.) Yes, at time t=0 years, V=12 because (1.25)^t=(1.25)^0=1
b.) You can look at successive years to find the rate.
At year 1, V=12(1.25)=15
Using time t=0 and time t=1, the rate of appreciation equals
(new value minus old value) divided by old value
R=%28V%5B1%5D-V%5B0%5D%29%2FV%5B0%5D=%2815-12%29%2F12=0.25
As a percentage, 0.25 equals 25%
c.)V[5]=12(1.25)^5=12(3.052)=$36.62.
d.)

Looks like about 8 years.
V[8]=12(1.25)^8=$71.53.