Answer:
Option C -
Step-by-step 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
Now, putting values from the table,
x=-2 and f(x)=12.5
....[1] '
x=-1 and f(x)=2.5
....[2]
Now, dividing [1] and [2]
![\frac{12.5}{2.5}=\frac{ab^{-2}}{ab^{-1}}](https://tex.z-dn.net/?f=%5Cfrac%7B12.5%7D%7B2.5%7D%3D%5Cfrac%7Bab%5E%7B-2%7D%7D%7Bab%5E%7B-1%7D%7D)
![5=b^{-1}](https://tex.z-dn.net/?f=5%3Db%5E%7B-1%7D)
Substitute in [2]
![2.5=a(0.2)^{-1}](https://tex.z-dn.net/?f=2.5%3Da%280.2%29%5E%7B-1%7D)
![a=2.5\times 0.2](https://tex.z-dn.net/?f=a%3D2.5%5Ctimes%200.2)
![a=0.5](https://tex.z-dn.net/?f=a%3D0.5)
So, The exponential function with a=0.5 and b=0.2 is
![f(x)=(0.5)(0.2)^x](https://tex.z-dn.net/?f=f%28x%29%3D%280.5%29%280.2%29%5Ex)
Therefore, Option C is correct.