Chapter 2.2, Problem 72E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### 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 of200 mg/dL (milligrams per deciliter). If the amount of alcohol in the blood decays exponentially, and after 2 hours, 112.5 mg/dL remain, find an exponential model for the person's blood alcohol level, and use your model to estimate the person's blood alcohol level after 4 hours. [HINT: See Example 2.]

To determine

To calculate: The exponential model for the person’s blood alcohol level and estimate the level after 4 hours if the amount of alcohol in the blood decays exponentially from 200 mg/dL to 112.5 mg/dL after 2 hours.

Explanation

Given Information:

The initial blood alcohol level is 200Ā mg/dL. The amount of alcohol in the blood decays exponentially from 200Ā mg/dL to 112.5Ā mg/dL after 2 hours.

Formula used:

Formula of exponential function is given by,

f(t)=Abt

Calculation:

Consider the formula of exponential function,

f(t)=Abt

Here f(t) blood alcohol level, A,b are constant and t is time.

Initially blood alcohol level was 200Ā mg/dL.

Substitute t=0 in f(t)=Abt:

f(0)=Ab0

Substitute f(0)=200Ā mg/dL and b0=1 in f(0)=Ab0:

200=A

Now, The amount of alcohol in the blood decays exponentially from 200Ā mg/dL to 112.5Ā mg/dL after 2 hours.

Substitute t=2 in f(t)=Abt:

f(2)=Ab2

Substitute f(2)=112

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