Given:
[tex]\frac{dx}{dt}=x+6[/tex]Let's find the time taken to transverse a distance of 96 units.
To find the distance, we have:
[tex]\int_0^{96}\frac{dx}{x+6}[/tex]Solving the integral, we have:
[tex]\begin{gathered} [ln(x+6)]_0^{96}=t \\ \\ \\ [ln(96+6)-ln(6))=t \\ \\ =ln(102)-ln(6)=t \\ \\ =\frac{ln(102)}{ln(6)} \\ \\ =ln(\frac{51}{3}) \\ \\ =ln(17) \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} ln(\frac{51}{3}) \\ \\ OR \\ \\ ln(17) \end{gathered}[/tex]