Question

A media company wants to track the results of his new marketing plan so the video production manager recorded the number of use for one of the companies online videos the results of the first five weeks are shown in this table..
Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x).

Answer 1

Answer:

$f(x)=5120(5)^{x}$

Step-by-step explanation:

From the image, f(x) and x are rlated by

$f(x)=a( {b})^{x}$

where b is the common ratio

We first find the value for b

$\frac{6400}{5120}= 5$

$\frac{8000}{6400}= 5$

$\frac{10000}{8000} = 5$

$\frac{12500}{10000} = 5$

$\frac{15625}{12500}=5$

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

$5120 = a(5)^{0}$

but

$5^{0} = 1$

Hence a=5120

Thus the equation which model the relationship between the weeks and the viewers is

$f(x)=5120(5)^{x}$