a.
To find: the thickness of aluminum shielding.
Given: The equation is
Concept used:
(1) A exponential model or function is defined as:
(2) By the product property of logarithm is as;
Calculation:
Now, simplify the above equation as follows:
rewrite this equation ;
Take logarithms on both sides with a natural base.
Thus,
Therefore,
Also given
These values are substituted in the above equation (2);
Thus,
Conclusion:
Hence, the thickness of aluminum shielding is
b.
To find: the thickness of copper shielding.
Given: The equation is
Concept used: (1) A exponential model or function is defined as:
(2) By the product property of logarithm is as;
Calculation:
Now, simplify the above equation as follows:
rewrite this equation ;
Take logarithms on both sides with a natural base.
Thus,
Therefore,
Also given
These values are substituted in the above equation (2);
Thus,
Conclusion:
Hence, the thickness of copper shielding is
c.
To find: the thickness of lead shielding.
Given:
The equation is
Concept used:
(1) A exponential model or function is defined as:
(2) By the product property of logarithm is as;
Calculation:
Now, simplify the above equation as follows:
rewrite this equation ;
Take logarithms on both sides with a natural base.
Thus,
Therefore,
Also given
These values are substituted in the above equation (2);
Thus,
Conclusion:
Hence, the thickness of lead shielding is
d.
To find: the result from (a) − (c) and also explain your best material.
Given:
The equation is
Concept used: A exponential model or function is defined as:
Calculation:
According to this question; part(a) − part(c)
Here, in part(a) thickness of aluminum material is
So,
Less lead is required to protect from the same amount of radiation for would need an aluminum apron
Conclusion:
Hence, the required result is
Chapter 4 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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