a.
To determine : if the sequence is arithmetic, geometric or neither if a scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
The sequence
Given information :
A scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
Formula used :
The common ratio of a geometric series is calculated as
Calculation :
Consider the sequence
Calculate the value of
As the common ratio is same, the series is a geometric series.
Thus, the sequence
b.
To calculate : the rule for
The rule for
Given information :
A scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
Formula used :
The
Calculation :
Consider the sequence
From part (a), the value of
Put the value
Thus, the rule for
c.
To graph: the sequence if a scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
Given information:
The given sequence is
Graph:
Consider the given sequence:
The terms represent the radioactive decay every two hours. So, the first hour can be considered as point 1.
These terms can be written as:
Now to draw the graph by plotting these points on the graph:
Interpretation: It can be seen that as
d.
To calculate : the time after which the scientist measures Platinum-197 that is less than 1 gram if a scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
The time after which the scientist measures Platinum-197 that is less than 1 gram is at most 7 hours.
Given information :
A scientist is studying the radioactive decay of Platinum-197. The scientist starts with 66-gram sample of Platinum-197 and then measures the amount remaining every two hours. The amount recorded are
Formula used :
The
Calculation :
From part (b), the rule comes out to be
It is needed to find a number such that
Take
The time required is at most 7 hours.
Thus, the time after which the scientist measures Platinum-197 that is less than 1 gram is at most 7 hours.
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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