Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

(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.

Sagot :

RedRicin
Here's the formula for exponential decay:

[tex]A = p(1-k)^t[/tex]

(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.

[tex]0.08 = 0.20(1-0.47)^t[/tex]

And now we solve for t.

[tex]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}[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.