Answer:
Option 3 and 5 are correct
Step-by-step explanation:
We have given a geometric series 640,160,40,10....
Common ratio of geometric series is [tex]r=\frac{a_2}{a_1}[/tex]
[tex]r=\frac{160}{640}=\frac{1}{4}<0[/tex]
Here our common ratio is less than zero
It will show the graph of exponential decay
Hence, option 5 is correct.
The general term of geometric series is [tex]a_n=a\cdotr^(n-1)[/tex]
Domain will be all natural numbers since, geometric series take only natural numbers.
Here, values of "n" is domain
Hence, option 3 is correct.
Range can be any positive real numbers not only natural number
Range is the value of [tex]a_n[/tex]
Hence, option 4 is discarded.
Graph can not be linear of a geometric series being exponential
Hence, option 2 is discarded.
Option 1 is discarded because it is exponential decay function so it can not be exponential growth.
Therefore, Option 3 and 5 are correct.
Answer:
The options that hold true are:
Step-by-step explanation:
We are given a geometric sequence as:
640, 160, 40, 10, ...
Clearly we see that each term is decreasing at a constant rate as compared to it's preceding term.
Hence, the graph formed by this sequence will be a exponential graph with decay .
( since, the terms of the sequence are decreasing)
The sequence could be modeled as:
Let [tex]a_n[/tex] represents the nth term of the sequence.
Hence,
[tex]a_n=640\cdot \dfrac{1}{4^{n-1}}[/tex]
As, the sequence is geometric hence the domain will be a set of natural numbers.
but the range will be positive real numbers.
Hence, the correct option is:
The domain will be the set of natural numbers.
The graph will show exponential decay
