Question

(Drinking and driving.) Just after Eric had his last drink, the alcohol level in his bloodstream was 0.20 (milligram of alcohol per milliliter of blood). The alcohol level A(t) in a person follows the exponential decay law. If the legal driving limit for alcohol level is 0.08, how long should Eric wait (after his last drink) before he will legally be able to drive? Let k = 0.47. Give answer in hours to two decimal places.

Answer 1

Here's the formula for exponential decay:

$A = p(1-k)^t$

(where A = new amount, p = principal (starting) amount, k = rate of decay, and t = time)

Let's use what we know and fill in the expression.

$0.08 = 0.20(1-0.47)^t$

And now we solve for t.

$0.08 = 0.20(0.53)^t \\ 0.4 = 0.53^t \\ log0.4=t*log0.53 \\ t = \frac{log0.4}{log0.53} = \boxed{1.44\ hours}$