4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{44035bf8-f54c-472a-b969-b4fa4fa3d203-10_677_839_251_516}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The number of subscribers to an online video streaming service, \(N\), is modelled by the equation
$$N = a b ^ { t }$$
where \(a\) and \(b\) are constants and \(t\) is the number of years since monitoring began.
The line in Figure 1 shows the linear relationship between \(t\) and \(\log _ { 10 } N\)
The line passes through the points \(( 0,3.08 )\) and \(( 5,3.85 )\)
Using this information,
- find an equation for this line.
- Find the value of \(a\) and the value of \(b\), giving your answers to 3 significant figures.
When \(t = T\) the number of subscribers is 500000
According to the model,
- find the value of \(T\)