Question

PLEASE HELP! ASAP!

Which exponential function is represented by the table?
A) f(x) = 0.2(0.5x)
B) f(x) = 0.5(5x)
C) f(x) = 0.5(0.2x)
D) f(x) = 0.2(0.2x)

Answer 1

C should be the answer, don't quote me on that though

Answer 2

Option C -
`f(x)=(0.5)(0.2)^x`

Explanation:

Given : The table of an exponential function.

To find : Which exponential function is represented by the table?

Solution :

First we create an exponential from the given table by taking any two values.

The general form of an exponential
`f(x)=ab^x`

Now, putting values from the table,

x=-2 and f(x)=12.5

`12.5=ab^(-2)` ....[1] '

x=-1 and f(x)=2.5

`2.5=ab^(-1)` ....[2]

Now, dividing [1] and [2]

`(12.5)/(2.5)=(ab^(-2))/(ab^(-1))`

`5=b^(-1)`

`b=(1)/(5)`

`b=0.2`

Substitute in [2]

`2.5=a(0.2)^(-1)`

`a=2.5* 0.2`

`a=0.5`

So, The exponential function with a=0.5 and b=0.2 is

`f(x)=(0.5)(0.2)^x`

Therefore, Option C is correct.