Since the amount of caffeine depreciates by 21% every hour, this is a case of exponential decay. The formula is expressed as
A(t) = Aoe^- rt
where
Ao = initial amount
r = rate of decay(the negative sign indicates decay)
t = time
From the information given,
Ao = 80
r = 21/100 = 0.21
Writing the function in terms of k and t, we have
k(t) = 80e^-0.21t
For 7 hours, we would substitute t = 7 into the function. We have
k(7) = 80e^- 0.21 * 7
k(7) = 80e^-1.47
