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Chapter 10: Q. 10.89 (page 1053)

The half-life of magnesium-27 is 9.45 minutes. How much of a 10-mg sample will be left in 6 minutes?

Short Answer

Expert verified

6.45mgof the sample will be left from 10mg in6minutes

Step by step solution

01

Step 1. Given information  

It is given that the half-life of the element is9.45minutes.

02

Step 2. Finding the value of k

For an original amount, A0, that grows or decays at a rate, localid="1645080842678" k, for a certain time, t, the final amount,

Then substituting the given values in the formula we get:

localid="1645079763896" A=A0ekt5=10e9.45k12=e9.45k

03

Step 3. Use logarithmic properties  

Taking logarithmic properties on both sides, we get:

12=e9.45kln12=lne9.45kln12=9.45klnea=a-0.699.45=kk=-0.073

04

Step 4. Finding the number of decreased bacteria 

Substituting the obtained value of k and the given time in the given formula, we get:

A=A0ektA=10e-0.073路6A=10e-0.438A=10路0.645A=6.45

role="math" localid="1645080094787" 6.45mgof the sample will be left in6minutes.

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