   Chapter 2.3, Problem 25E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

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

In Exercises 21-26, find the associated half-life or doubling time. [HINT: See Quick Examples 11-18.] Q = Q 0 e − 4 t

To determine

To calculate: The associated half-life time or doubling time of the model if Q=Q0e4t.

Explanation

Given Information:

The associative exponential decay model is Q=Q0e4t.

Formula used:

An exponential decay function has the form,

Q(t)=Q0ekt

Here, Q(t) is the remaining amount, Q0 is the value of Q at time t=0 and k is the decay constant.

The growth constant k and doubling time td for Q are related as,

tdk=ln2

Calculation:

Consider the provided model,

Q=Q0e4t

Here the value of k is negative so that it is an exponential decay model.

Compare the give decay model with the standard decay model Q(t)=Q0ekt to find decay constant

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