Question 39485This question is from textbook
: Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Using the index of a series as the domain and the value of the series as the range, is a series a function?
Yes, because each index value(The number of the term) there is one value(the
term itself).
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Linear because each successive term has a common difference. This difference
corresponds to the slope of a linear function.
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series? a(n)=[a(1)]r^(n-1) indecating a consistent
multiply of the 1st term be successive powers of the ratio r.
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Arithmetic: Cost associated with a quantity of a particular item.
For example Cost = 10x is the cost of x-number of an item that cost $10.
Personal impact. Buy more of a kind and it will cost you more.
Geometric: Value of a money account after n periods of compounding at annual interest "i".
Value=(initial investment)(1+i)^(n)
Very important to understand the powerful building power of compounded savings.
For example of the $22 given to the American Indians for the right of Dutch
settlers to stay on Manhatten Island had been invested in a compound interest
account at that time it would be worth enough now to purchase all the property
on Manhattan Island.
Cheers,
Stan H.
Cheers,
Stan H.
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