Question

640, 160, 40, 10, ...

Answer 1

Answer:

The options that hold true are:

• The domain will be the set of natural numbers.  

• The graph will show exponential decay.

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 $a_n$ represents the nth term of the sequence.

Hence,

$a_n=640\cdot \dfrac{1}{4^{n-1}}$

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

Answer 2

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 $r=\frac{a_2}{a_1}$

$r=\frac{160}{640}=\frac{1}{4}$

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 $a_n=a\cdotr^(n-1)$

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 $a_n$

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.