Chapter 1.1, Problem 43E

(a)

To determine

To calculate: The value of $p\left(4.5\right)$ by draw the graph and interpret the answer. The table below shows the data for the popularity of twitter in social media sites as rated by Stat.counter.com ($t$ is the number of years since the start of the year $2008$

).

$\begin{array}{ccccc}\begin{array}{l}\text{Year }t\\ \left(\text{year since 2008}\right)\end{array}& 1& 2& 4& 5\\ \text{Twitter Popularity }p\left(t\right)\left(\%\right)& 7& 6& 6& 7\end{array}$

(b)

To determine

The model which exactly fits the provided data.

$\begin{array}{ccccc}\begin{array}{l}\text{Year }t\\ \left(\text{year since 2008}\right)\end{array}& 1& 2& 4& 5\\ \text{Twitter Popularity }p\left(t\right)\left(\%\right)& 7& 6& 6& 7\end{array}$

The options are:

$\begin{array}{l}\left(\text{A}\right)0.4t^3-4t^2+12.5t+15\\ \left(\text{B}\right)-0.33t^2+2t-8.7\\ \left(\text{C}\right)-0.4t^3+4t^2-12.5t+15\\ \left(\text{D}\right)0.33t^2-2t+8.7\end{array}$