Answer:
[tex]f(x)=5120(5)^{x} [/tex]
Step-by-step explanation:
From the image, f(x) and x are rlated by
[tex]f(x)=a( {b})^{x}[/tex]
where b is the common ratio
We first find the value for b
[tex] \frac{6400}{5120}= 5[/tex]
[tex] \frac{8000}{6400}= 5[/tex]
[tex] \frac{10000}{8000} = 5 [/tex]
[tex] \frac{12500}{10000} = 5[/tex]
[tex] \frac{15625}{12500}=5[/tex]
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
[tex]5120 = a(5)^{0} [/tex]
but
[tex]5^{0} = 1 [/tex]
Hence a=5120
Thus the equation which model the relationship between the weeks and the viewers is
[tex]f(x)=5120(5)^{x} [/tex]
