o The total time T (in hours) of the trip as a function of the distance x (in miles). Make sure you show all your work to come up with this equation, and explain each step and what it represents.

o The domain of the function. Explain why this domain makes sense, and show work as needed.

o Graph the function using the graphing utility on Desmos.com. Take a screenshot and make sure it is included in your document. The graph should be focused over the domain of the function.

o Find the value of x that minimizes T. Desmos.com will note this ordered pair for you automatically. If it does not, then you can click various points of the graph and it will display the ordered pair.

o What does the ordered pair of the minimum for T represent in our situation? I.E. what does the value of x tell us, and what does the value of T tell us? Write a brief paragraph interpreting these values.

10. Trip Time You are in a boat2 miles from the nearest point on the coast (see

figure). You plan to travel to point 2,3 miles down the coast and 1 mile inland.

You row at 2 miles per hour and walk at 4 miles per hour.

2 mi

1 mi

3 mi

Q

Nor drawn to scale

a. Write the total timet (in hours) of the trip as a function of the distance x (in

miles).

b. Determine the domain of the function.

c. Use a graphing utility to graph the function. Be sure to choose an

appropriate viewing window.

d. Find the value of that minimizes T.

e. Write a brief paragraph interpreting these values.