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Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid consumption of 30 mL of ethanol (corresponding to two standard alcoholic drinks).

The table shows the data they obtained by averaging the BAC (in mg/mL) of the eight men.

(a) Use the readings to sketch the graph of the BAC as a function of $ t $.(b) Use your graph to describe how the effect of alcohol varies with time.

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Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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researchers measured the blood alcohol concentration of eight adult male subjects after rapid consumption of thirty nose of ethanol. The table shows the data they obtained by averaging the ABC of the men, so use the readings to sketch the graph of the sea as a function of time. And so, looking at this table here, um, looks like we'LL construct a rough sketch of it. So we're in increments of Point Tio on. Maybe not quite twenty five twenty five. Okay, so it looks like a B a C increases and hasn't max at Aah! One hour. Oh, no points in five hours, three quarters of an hour and then slowly decreases and funneling when you're at four hours of beach, Uh, your base you is practically nothing. Let's go ahead and love Mathis here. So this is just a rough sketch. Maybe this point will be at the max, which we said was point seven five. You would do it here point by Yeah, some other points, Teo So for would be here. And so maybe point for the right here looks and it looks like yeah, graft will look something this about like that. So this report a hell for part B. Use a graft to describe how the effect about call berries with time and so looks like you know, you get this rabbit increase. Ah, you know, let in less than an hour and then after your maximum here Ah, the remaining three and a quarter hours of your B A C decreases over time.

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