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 ![r=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
![r=\frac{160}{640}=\frac{1}{4}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B160%7D%7B640%7D%3D%5Cfrac%7B1%7D%7B4%7D%3C0)
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 ![a_n=a\cdotr^(n-1)](https://tex.z-dn.net/?f=a_n%3Da%5Ccdotr%5E%28n-1%29)
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 ![a_n](https://tex.z-dn.net/?f=a_n)
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.