Q(t) = 40((e^-t) - (e^-2t))
For q(t) to be maximum dq/dt = 0
dq/dt = 40(-(e^-t) + 2(e^-2t) = 0
2e^-2t - e^-t = 0
2e^-2t = e^-t
e^t = 2
t = ln 2
q(ln 2) = 40((e^(-ln 2) - (e^(-2ln 2)) = 40(1/2 - 1/4) = 40(1/4) = 10
Therefore, thw maximum amount of drug in the bloodstream at one time is 10 mg.
The probability is still calculated the same way, using the number of possible ways to outcome can occur divided by the total number of outcomes.
The doubling time is a characteristic unit (a natural unit of scale) for the exponential growth equation, and its converse for exponential decay is the half-life. For example, given Canada's net population growth of 0.9% in the year 2006, dividing 70 by 0.9 gives an approximate doubling time of 78 years.
