ThequadraticfunctionG=f(s),0s20, expresses the number of gallons of gas in your tank in terms of your distance (in miles) from Shoreline as you drive north in traffic on I-5from Shoreline toward Everett between 9 am and 10 am.

(a) Find a possible and reasonable expression for the function that satisfies the following conditions:

i) Your average gas mileage for the 20-mile trip is 10 miles/gal.

ii) Your (instantaneous) gas mileage is at least 14 miles/gal for some part of the trip.1

iii) Your gas mileage is never more than 40 miles/gal. (Unless modified by average, gas mileage always refers to your instantaneous mileage).

iv) You have enough gas to make the 20-mile trip back to Shoreline. See the last part of this problem for information about the return trip.

v) There is at least one other condition to consider, but this is left for you.

Check that your function meets these conditions. Be sure to explain how you went about finding your function.

(b) On separate coordinate systems, graph the functionG=f(s)and the function that expresses your gas mileage in terms of. Be sure to state the latter function and explain how you found it.

(c) Find a quadratic functions=h(t),0t1, that expresses your distance from Shoreline as a function of the number of hours since 9:00 that meets the following conditions:

i) Your speed is always between 5 miles/hour and 50 miles/hour.

ii) Your function is compatible with the assumption that between these speeds a small increase in the speed improves your gas mileage.

iii) There is one other condition that comes from the statement of the problem. Check that your function meets these conditions. Explain how you went about finding your function.

(d) There is less traffic on your way home from Everett to Shoreline, and at each point of the return trip your gas mileage is 25%greater than it was at the same point on the outbound trip. Use your function from part a) to find another functionG=w(s),0s20, that expresses the number of gallons in your tank in terms of your distance from Shoreline on the return trip. Assume you did not get gas during the day and that you drive a negligible distance getting to and from I-5. Graph this function.