   Chapter 4.6, Problem 1CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Checkpoint 1 Worked-out solution available at LarsonAppliedCalculus.comUse the model in Example 1 to determine the number of years required for a 1-gram sample of radium to decay to 0.4 gram.

To determine

To calculate: The number of years needed to decay a sample of 1-gram of radium to 0.4 gram.

Explanation

Given Information:

The sample of 1-gram of radium decay to 0.4 gram

Formula used:

Exponential growth and decay:

If the rate of change of a positive quantity y with respect to time is proportional to the amount of quantity present at any time t, that is dydt=ky, then y is given by the equation, y=Cekt, where C is the value of the quantity at time t=0 and k is the constant of proportionality.

If k>0 then there is exponential growth and when k<0 then there is exponential decay.

Calculation:

Consider the equation, y=Cekt.

Substitute y=1 and t=0 in the equation y=Cekt.

1=Cek×01=C

Here, the half-life of radium is 1599 years.

Substitute y=12 and t=1599 in the equation y=Cekt.

12=Ce1599k

Take natural log on both the sides,

ln(e1599k)=ln(12)1599k(ln<

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