Answer: The graph of the P(t) has been provided, we have to find the instantaneous slope of P(t) at t = 8:
[tex]Slope=m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore we need two y values and two x values, which can be obtained as follows:
[tex]\begin{gathered} t=8 \\ \\ \therefore\Rightarrow \\ \\ x_1=t_1=8-0.1=7.9 \\ \\ y_1=P(t_1)=P(7.9) \\ \\ x_2=t_2=8+0.1=8.1 \\ \\ y_2=P(t_2)=P(8.1) \\ \\ \therefore\rightarrow \\ \\ Slope=\frac{P(8.1)-P(7.9)}{t_2-t_1}\rightarrow(1) \\ \end{gathered}[/tex]
Equation (1) corresponds to the third, option, therefore that is the answer.
