Answer:
![f(x)=5120(5)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5120%285%29%5E%7Bx%7D%20)
Step-by-step explanation:
From the image, f(x) and x are rlated by
![f(x)=a( {b})^{x}](https://tex.z-dn.net/?f=f%28x%29%3Da%28%20%7Bb%7D%29%5E%7Bx%7D)
where b is the common ratio
We first find the value for b
![\frac{6400}{5120}= 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B6400%7D%7B5120%7D%3D%205)
![\frac{8000}{6400}= 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B8000%7D%7B6400%7D%3D%205)
![\frac{10000}{8000} = 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B10000%7D%7B8000%7D%20%3D%205%20)
![\frac{12500}{10000} = 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B12500%7D%7B10000%7D%20%3D%205)
![\frac{15625}{12500}=5](https://tex.z-dn.net/?f=%20%5Cfrac%7B15625%7D%7B12500%7D%3D5)
so we can say the common ratio, b=5
we put in any value of f(x) and the corresponding value for x to find a value
Let put x=0 and f(x)=5120
This implies that
![5120 = a(5)^{0}](https://tex.z-dn.net/?f=5120%20%3D%20a%285%29%5E%7B0%7D%20)
but
![5^{0} = 1](https://tex.z-dn.net/?f=5%5E%7B0%7D%20%3D%201%20)
Hence a=5120
Thus the equation which model the relationship between the weeks and the viewers is
![f(x)=5120(5)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5120%285%29%5E%7Bx%7D%20)