Question 1171696
formula for half life is:
1/2 = (1 + r) ^ n
when n = 3, the formula becomes:
1/2 = (1 + r) ^ 3
solve for r to get:
r = (1/2) ^ (1/3) - 1 = -.206299474.
that's your growth rate per time period.
confirm by replacing r in the original equation to get:
1/2 = (1 + r) ^ 3 becomes:
1/2 = (1 - .206299474) ^ 3 = 1/2
this confirms the value of r is good.


to find how long the patient has to wait for there to be only 6.25% of the original dose in his system, the the formula becomes.
.0625 = 1 * (1 - .206299474) ^ n
simplify to get:
.0625 = (1 - .206299474) ^ n
take the log of both sides of the equation to get:
log(.0625) = log((1-.206299474)^n)
since log(x^n) = n * log(x), this becomes:
log(.0625) = n * log(1 - .206299474)
solve for n to get:
n = log(.0625) / log(1 - .206299474) = 12.
confirm by replacing n in the original equation to get:
.0625 = (1 - .206299474) ^ n becomes:
.0625 = (1 - .206299474) ^ 12 = .0625
this confirms the value of n is good.


your solution is that the patient will have to wait 12 hours before taking another dose.