The concentration (in milligrams per liter) of a medication in a patient’s…

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The concentration

C

(in milligrams per liter) of a medication in a patient’s bloodstream at time

t

hours after administration is monitored periodically. The data collected near

t=8

hours are shown below.

$t$ (hours)	$8.01$	$8.005$	$8.002$	$8$ (—)	$7.998$	$7.995$	$7.99$
$C(t)$ (mg/L)	$2.413$	$2.410$	$2.409$	—	$2.404$	$2.401$	$2.396$

(The dash indicates that the concentration was not measured exactly at

t=8

hours.) (a) Determine a numerical estimate of

\displaystyle \lim_{t\to 8^+} C(t)

. (b) Interpret the value found in part (a) in the medical context of the problem. (c) Discuss one factor inherent in the data that could affect the reliability of your estimate.

Related theory

Limits
Existence of a limit
Limits and Derivatives
Limits and Continuity

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