ANSWER
[tex]3.9705\text{ seconds}[/tex]EXPLANATION
To find how many seconds it will take to travel 71 feet, substitute the value of d to be 71 feet and solve for t in the equation:
[tex]\begin{gathered} 71=2t+4t^2 \\ \Rightarrow4t^2+2t-71=0 \end{gathered}[/tex]Solve for t using the Quadratic formula:
[tex]a=4,b=2,c=-71[/tex]Therefore, we have:
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-2\pm\sqrt[]{2^2-(4\cdot4\cdot-71)}}{2\cdot4} \\ t=\frac{-2\pm\sqrt[]{4+1136}}{8}=\frac{-2\pm\sqrt[]{1140}}{8} \\ \Rightarrow t=\frac{-2+33.7639}{8};t=\frac{-2-33.7639}{8} \end{gathered}[/tex]Since time cannot be negative, we only use the first value:
[tex]\begin{gathered} t=\frac{-2+33.7639}{8}=\frac{31.7639}{8} \\ t=3.9705\text{ seconds} \end{gathered}[/tex]That is the time it will take.
