MATLAB PLEASE$<mn\; id="EditorElement\_10647110">3</mn>$

Use MATLAB to complete the following and state answers in complete sentences using either "disp" or "fprintf" commands. Be sure only hard code the given information. Label values in your code appropriately and write comments where necessary. An exponential bike ride Tom and Sue took a bike ride, both starting at the same time and position. Tom started riding at$,$ and his velocity decreased according to the function, for $.$ Sue started riding at $15,$ and her velocity decreased according to the function, for $.$

a$.$ Determine the position functions for both Tom and Sue.

b$.$ Graph the position functions of Tom and Sue on the same set of axes.

c$.$ Aside from start, determine when and where Tom and Sue will meet along their bike ride.

d$.$ Who ultimately took the lead and remained in the lead? $($Consider limits as time approaches infinity.$)$

Tips:

Theorem $6\mathrm{.}1$ in the textbook uses a definite integral and initial position to produce the position function. This will be more efficient than programming MATLAB to produce the correct $C-$value for an antiderivative.

Commands for graphing are on pp$.5-7$ in the guide. $($continued on next page$)$

Keep in mind what units of measure are associated with this problem and be sure to include them on your graph's axes and within your final statements in the Command window.

$-$When equations have more than one solution, remember that you can call in a specific solution by adding a number in parentheses after the name, e$.$g$.$ Time$\_$of$\_$Intersection$(1).$

The last part of this assignment asks you to consider the limits of each person's position as time increases. In order to state who remains in the lead, try comparing the two limits with an if$-$else statement.