SOLUTION: The annual consumption of frozen yogurt has decayed approximately exponentially from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006. Predict when the consumption wil

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Question 668817: The annual consumption of frozen yogurt has decayed approximately exponentially from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006. Predict when the consumption will be 0.5 pounds per person. Show steps.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The annual consumption of frozen yogurt has decayed approximately exponentially
from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006.
:
Use the exponential decay formula using e
Ao*e^(-t/k} = A, where
Ao = initial amt
A = resulting amt after t time
t = time in yrs
k = constant of decay of substance
:
t = 11 yrs (1995 to 2006)
2.6*e^(-11/k) = 1
Divide both sides by 2.6
e^(-11/k) = .3846
nat log of both sides (ln of e = 1)
-11%2Fk = ln(.3846)
-11%2Fk = -.9555
k = %28-11%29%2F%28-.9555%29
k = +11.512 is the constant of decay
:
Predict when the consumption will be 0.5 pounds per person.
k = 11.512, find t
2.6*e^(-t/11.512) = .5
Divide both sides by 2.6
e^(-t/11.512) = .1923
Nat logs of both sides
-t%2F11.512 = -1.6487
t = -1.6487 * -11.512
t ~ 19 yrs from 1995; 2014, the year when consumption is only .5 lb