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.
: 
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/k}}} = ln(.3846)
{{{-11/k}}} = -.9555
k = {{{(-11)/(-.9555)}}}
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/11.512}}} = -1.6487
t = -1.6487 * -11.512
t ~ 19 yrs from 1995; 2014, the year when consumption is only .5 lb