we can do a rough estimate this way:
now she has 0.28 mg of alcohol in her blood, after 2 hours she will have (1/2)0.28 = 0.14 mg. after another 2 hours, she will have (1/2)0.14 = 0.07 mg. This is under the limit, so she needs to wait for just under 4 hours before driving.
if we want to be more specific, we have to make an equation.
Let be the amount of alcohol per mL of blood remaining after time
Let be the initial amount of alcohol in her blood
After each half-life period, we will have some multiple of 1/2 of the original amount remaining. so if we start with after two hours, we have after two more hours, we have , so we can come up with a general formula. since for half-life periods, is some multiple of 1/2 times , we get:
Now, when (which is the half-life), we have half the original amount remaining, so , so plug these values in.
equating coefficients we get:
So finally, our formula is:
We want when , so we get: