Question

A media company wants to track the results of its new marketing plan, so the video production manager recorded the number of views for one of the company's online videos. The results of the first 5 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). Enter the correct answer in the box by replacing the values of a and b.

Answer 1

`f(x)=5120\cdot1.25^x`

Step-by-step explanation

We want to write an equation that models the relationship between the number of weeks (x) and the number of views, f(x).

From the table, we see that the relationship of the two terms (number of views and number of weeks) is exponential.

The general form of an exponential function is given as:

`f(x)=a\cdot b^x`

where a = initial value

b = exponential factor

We have to find a and b.

We do this by replacing x and f(x) in the function with values from the table.

Let us use the first set of values:

`\begin{gathered} 5120=a\cdot b^0 \\ \Rightarrow5120=a\cdot1 \\ \Rightarrow a=5120 \end{gathered}`

We have found the value of a, now we can find the value of b by using another set of values from the table.

That is:

`\begin{gathered} 6400=5120\cdot b^1 \\ 6400=5120\cdot b \\ \text{Divide both sides by 5120:} \\ b=(6400)/(5120) \\ b=1.25 \end{gathered}`

Now, we have found a and b.

Therefore, the equation that models the relationship between number of views and number of weeks is:

`f(x)=5120\cdot1.25^x`