Question

Which description matches the function represented by the values of the table

Answer 1

The function is
`y=3.5(4)^x` and is an exponential growth model.

Explanation:

Given : The data representing a function.

We have to choose the correct option from the given options that describes the values in the given table.

Consider the given table,

x y

1 14

2 56

3 224

4 896

5 3584

Since, The value of y is increasing with increasing value of x.

So, It is a growth function.

Also, The function for exponential growth is represented by function.

`y=cb^x`

Let us consider any two points out of given points (2,56) and (3,224)

Then

`56=cb^2` and
`224=cb^3`

Divide both equations, we have,

`(224)/(56)=(cb^3)/(cb^2)`

Simplify, we have,

b = 4

Now substitute value of b in any of equation

`56=c(4)^2=16c`

Divide both side by 16 , we have,

c = 3.5

Thus, The function is
`y=3.5(4)^x` and hence, is an exponential growth model.

Answer 2

It is an exponential growth

Therefore, option C is correct.

Explanation:

The given function is increasing hence, it can not be decay

So, option A and D are incorrect being decay.

Now, the given function is:

taking two points

(1,14) and (2,56)

y=ab

`14=ab` (1)

And
`56=ab^2` (2)

Divide 2 by 1 we get:

`4=b`

Hence,
`a=(y)/(b)`

Now, taking point (1,14)

`a=(14)/(4)=(7)/(2)`

So, the function is:

`y=(7)/(2)\cdot 4^x`

Hence, it is an exponential growth

Therefore, option C is correct.