Chapter ISG, Problem 7.9.2P

To determine

To graph: an example of the given situation.

Answer to Problem 7.9.2P

The functions that represent the given situation will be:

  $f(n)=8\times {(\frac{1}{2})}^{n-1}$ And $g(n)=8\times 2^{n-1}$ .

Explanation of Solution

Given information: Given situation is, Consider two different geometric sequences.

Each starts with the same constant. The common ratio producing subsequent terms in the first is positive and is the reciprocal of the common ratio producing subsequent terms in the second

Calculation:

Let first geometric sequence is 8, 4, 2, 1……… $8\times {(\frac{1}{2})}^{n-1}$ .

Second geometric sequence is 8, 16, 32, 64…… $8\times 2^{n-1}$ .

These two sequence satisfies the given situation as both sequence starts with same constant term that is 8 and common ratio producing subsequent terms in the first is (1/2) that is positive and is the reciprocal of the common ratio producing subsequent terms in the second that is 2.

So, the function that represents the both sequence is:

  $f(n)=8\times {(\frac{1}{2})}^{n-1}$ And $g(n)=8\times 2^{n-1}$ .

The graph of both the function using graphing utility is given below.

  

Blue line curve shows function $f(n)=8\times {(\frac{1}{2})}^{n-1}$ .

Red line curve shows function $g(n)=8\times 2^{n-1}$ .