Solve your doubts and expand your knowledge with Westonci.ca's extensive Q&A database. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

## Sagot :

[tex]\[ f(x) = a \cdot b^x \][/tex]

Here, [tex]\(a\)[/tex] represents the initial number of views when [tex]\(x = 0\)[/tex], and [tex]\(b\)[/tex] represents the growth factor per week.

Based on the given data and calculations, we find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

From the table:

[tex]\[ \begin{array}{|c|c|} \hline \text{Weeks}, \; x & \text{Views}, \; f(x) \\ \hline 0 & 5{,}120 \\ \hline 1 & 6{,}400 \\ \hline 2 & 8{,}000 \\ \hline 3 & 10{,}000 \\ \hline 4 & 12{,}500 \\ \hline 5 & 15{,}625 \\ \hline \end{array} \][/tex]

We can determine the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:

- [tex]\(a\)[/tex] is the initial value when [tex]\(x = 0\)[/tex], which is [tex]\(5{,}120\)[/tex].

- [tex]\(b\)[/tex] is the growth rate, which is approximately [tex]\(1.25\)[/tex].

Thus, substituting [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the exponential function:

[tex]\[ f(x) = 5119.999999999992 \cdot (1.2499999999999998)^x \][/tex]

For simplicity, we can round the coefficients to:

[tex]\[ f(x) = 5120 \cdot 1.25^x \][/tex]

This equation models the relationship between the number of weeks [tex]\(x\)[/tex] and the number of views [tex]\(f(x)\)[/tex]:

[tex]\[ \boxed{f(x) = 5120 \cdot 1.25^x} \][/tex]