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Math
CalculusFinite Mathematics and Applied Calculus (MindTap Course List)7th Edition

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Chapter 2.3, Problem 58E
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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section
Problem 1E
Problem 2E
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Problem 4E
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Problem 6E
Problem 7E
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Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
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Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
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Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
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Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Alcohol After a large number of drinks, a person has a blood alcohol level of 200 mg/dL (milligrams per deciliter). If the amount of alcohol in the blood decays exponentially, with one fourth being removed every hour, find the time it will take for the person's blood alcohol level to decrease to 80mg/dL.

To determine

To calculate: The time it will take the level of alcohol to decrease to 80 mg/dL if initially patient has absorbed 200 mg of the alcohol and one by fourth of the remaining alcohol is being removed every hours.

Explanation

Given Information:

The alcohol in the blood decays exponentially. One by fourth of the remaining alcohol is being removed after every hours. The patient has alcohol level 200Ā mg/dL in the blood initially. The final alcohol level is 80Ā mg/dL.

Formula used:

The expression of exponential decay model is,

Q(t)=Q0eāˆ’kt

Here, Q(t) is remaining amount at time t, Q0 is initial amount of the sample, k is decay constant and t is time in year.

The relation between decay constant and half-life time is,

tdk=ln2

Here, td is half-life time.

Calculation:

Consider the expression of exponential decay model

Q(t)=Q0eāˆ’kt

Since One by fourth of the remaining alcohol is being removed after every hours. Therefore after one hour reaming alcohol contain in the patient is,

Q=Q0(1āˆ’14)=34Q0

Therefore substitute t=1 and Q=34Q0 in the expression Q(t)=Q0eāˆ’kt.

34Q0=Q0eāˆ’k(1)

Divide both side by Q0

34Q0Q0=Q0eāˆ’kQ034=eāˆ’k

Take natural log on both side of the equation

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Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E
Sect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.1 P-37ESect-2.1 P-38ESect-2.1 P-39ESect-2.1 P-40ESect-2.1 P-41ESect-2.1 P-42ESect-2.1 P-43ESect-2.1 P-44ESect-2.1 P-45ESect-2.1 P-46ESect-2.1 P-47ESect-2.1 P-48ESect-2.1 P-49ESect-2.1 P-50ESect-2.1 P-51ESect-2.1 P-52ESect-2.1 P-53ESect-2.1 P-54ESect-2.1 P-55ESect-2.1 P-56ESect-2.1 P-57ESect-2.1 P-58ESect-2.1 P-59ESect-2.1 P-60ESect-2.1 P-61ESect-2.1 P-62ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.2 P-58ESect-2.2 P-59ESect-2.2 P-60ESect-2.2 P-61ESect-2.2 P-62ESect-2.2 P-63ESect-2.2 P-64ESect-2.2 P-65ESect-2.2 P-66ESect-2.2 P-67ESect-2.2 P-68ESect-2.2 P-69ESect-2.2 P-70ESect-2.2 P-71ESect-2.2 P-72ESect-2.2 P-73ESect-2.2 P-74ESect-2.2 P-75ESect-2.2 P-76ESect-2.2 P-77ESect-2.2 P-78ESect-2.2 P-79ESect-2.2 P-80ESect-2.2 P-81ESect-2.2 P-82ESect-2.2 P-83ESect-2.2 P-84ESect-2.2 P-85ESect-2.2 P-86ESect-2.2 P-87ESect-2.2 P-88ESect-2.2 P-89ESect-2.2 P-90ESect-2.2 P-91ESect-2.2 P-92ESect-2.2 P-93ESect-2.2 P-94ESect-2.2 P-95ESect-2.2 P-96ESect-2.2 P-97ESect-2.2 P-98ESect-2.2 P-99ESect-2.2 P-100ESect-2.2 P-101ESect-2.2 P-102ESect-2.2 P-103ESect-2.2 P-104ESect-2.2 P-105ESect-2.2 P-106ESect-2.2 P-107ESect-2.2 P-108ESect-2.2 P-109ESect-2.2 P-110ESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.3 P-50ESect-2.3 P-51ESect-2.3 P-52ESect-2.3 P-53ESect-2.3 P-54ESect-2.3 P-55ESect-2.3 P-56ESect-2.3 P-57ESect-2.3 P-58ESect-2.3 P-59ESect-2.3 P-60ESect-2.3 P-61ESect-2.3 P-62ESect-2.3 P-63ESect-2.3 P-64ESect-2.3 P-65ESect-2.3 P-66ESect-2.3 P-67ESect-2.3 P-68ESect-2.3 P-69ESect-2.3 P-70ESect-2.3 P-71ESect-2.3 P-72ESect-2.3 P-73ESect-2.3 P-74ESect-2.3 P-75ESect-2.3 P-76ESect-2.3 P-77ESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ECh-2 P-1RECh-2 P-2RECh-2 P-3RECh-2 P-4RECh-2 P-5RECh-2 P-6RECh-2 P-7RECh-2 P-8RECh-2 P-9RECh-2 P-10RECh-2 P-11RECh-2 P-12RECh-2 P-13RECh-2 P-14RECh-2 P-15RECh-2 P-16RECh-2 P-17RECh-2 P-18RECh-2 P-19RECh-2 P-20RECh-2 P-21RECh-2 P-22RECh-2 P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-50RE

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