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Drinking and driving In a medical study, researchers measured the mean blood alcohol concentration (BAC) of eight fasting adult male subjects (in mg/mL) after rapid consumption of 30 $\mathrm{mL}$ of ethanol (corresponding to two standard alcoholic drinks). The BAC peaked after half an hour and the table shows measurements starting after an hour.$$\begin{array}{|c|c|c|c|c|c|}\hline t \text { hours) } & {1.0} & {1.25} & {1.5} & {1.75} & {2.0} \\ \hline \mathrm{BAC} & {0.33} & {0.29} & {0.24} & {0.22} & {0.18} \\ \hline\end{array}$$$$\begin{array}{|c|c|c|c|c|c|}\hline \text { t(hours) } & {2.25} & {2.5} & {3.0} & {3.5} & {4.0} \\ \hline \mathrm{BAC} & {0.15} & {0.12} & {0.069} & {0.034} & {0.010} \\ \hline\end{array}$$(a) Make a scatter plot and a semilog plot of the data.(b) Find an exponential model and graph your model with the scatter plot. Is it a good fit?(c) Use your model and logarithms to determine when the BAC will be less than 0.08 $\mathrm{mg} / \mathrm{mL}$ , the legal limit for driving.

(a) See plot(b) Yes, it is quite a good fit.(c) 2.6 hours

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

Baylor University

Idaho State University

Boston College

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All right, So you have blood concentration or alcohol. And so the model concentration populations is they're an exponential. So we have B for blood concentrations. Who is going to be some initial value Thames exponential to some coefficient. Alfa T, this is, uh, my sharing ours. Ours. So we have. Ah. So you have fear that they have live 1.5 hours. So Daddy's Salinas is that it digs Oh, 1.5 hours for dark concentration to reach our off the show concentration. So these right here, that's the love concentration 1.5 ours. She's there oflife, so we'll buy the engine. Half life is when that which is a couple of the initial concentration. Also, from here we come. You can solve that. So if you out what is this coefficient? You guys all day use your concentrations. And then from there we have We have this equation, Theo. Them's one by Balto 1/2 Which Europe line Natural. Order them both sides of the equation. We'll get we'll patrol over there. Won't be so We're all fucked. Times 1.5, Balto naturally one. And so? So he's gonna be able to Lloyd now I'm not divided. Bye. One point. Um, so computing that number, that's roughly Yeah, mind us. Oh, or 62 So these are all false? All they're asking us find exponential decay of model. So these is what they're calling there, What we're calling being. So this is a sea blood alcohol concentration on the well you have or Alfa. But we need to figure out there you nuts. And so the way that we can do that is does have another piece of information? No. So you know that your blood, our situation is point seeks your grams per millimetre. Oh, on our later Louisiana. So an hour later, it's that So that means that what he's saying is that or the called the time we're where we started measuring time, zero. That would be saying that this replacing what is what is, uh so this is a times so they're nothing. So this is saying that this should be equal to or six well off her cancer. In the units, it's people 21216 So we disagree Asian. We can't figure out what is not so counseling the exponential though the same US born six invited, but the mind knows. Point or six, two, one. Thanks. He soon all of it. That's mine. You think so? Is that but so we know that from these from this equation you have done these number Balto Marshal, over the mall. One, Huh? So you can use it. Get what is we got? Number will be the same. Teo. Naturally, one house. So these number here, that is that is just one house. So these home number here, the ground search going So this is the same us. Not with this. It was Boyd six. The way you're black. 1/2 which is the same. It's going to blind, but still No. So, Oh, separating off That is that we're here. Not with you equal to one or two, which is or six times. And so you have. You have that? Are you insane? It's gonna be one or two. That was to them. Line us boy for oh two. Christine, this is this part. So order terminating this part. This dysfunction looks like that thing. Explain, Shar. So it's gonna be something over these farm. So the initial initial value you, the vehicles here should be warned 0.2 so there's no way this is gonna be or going to the number on them. Also would like, uh So then we have here this society 1.2 on then if it is legal, too to drive off the that concentration, you need extent, we're here. That's it. Love, concentration. This is the time. So you have a photograph, then you need to find, say that is not evidently is not up to scale. Skill is not correct. Would say that this point were 0.28 when you will need Teo Trace Trey's that point or something. So at that point, well, this is their team. Not that we're looking for you say we call this time not the point from where it is legal to start driving is old that point right there? That is there your tina So it's a matter of praise tracing the girl from finding for which point on they continue here because situation is going to be smaller than point Hoyt. Well, you can ensure that because he needs that increasing function

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