Respuesta :

Answer:

 It is an exponential growth

Therefore, option C is correct.

Step-by-step 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

[tex]14=ab[/tex]     (1)

And [tex]56=ab^2[/tex]    (2)

Divide 2 by 1 we get:

[tex]4=b[/tex]

Hence, [tex]a=\frac{y}{b}[/tex]

Now, taking point (1,14)

[tex]a=\frac{14}{4}=\frac{7}{2}[/tex]

So, the function is:

[tex]y=\frac{7}{2}\cdot 4^x[/tex]

Hence, it is an exponential growth

Therefore, option C is correct.


Answer:

The function is [tex]y=3.5(4)^x[/tex] and  is an exponential growth model.

Step-by-step 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.

[tex]y=cb^x[/tex]

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

Then

[tex]56=cb^2[/tex] and [tex]224=cb^3[/tex]

Divide both equations, we have,

[tex]\frac{224}{56}=\frac{cb^3}{cb^2}[/tex]

Simplify, we have,

b = 4

Now substitute value of b in any of equation

[tex]56=c(4)^2=16c[/tex]

Divide both side by 16 , we have,

c = 3.5

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

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