Directions: Complete the two problems. Post your answers for either one in the appropriate forum, and discuss the methods you used. Interpret your answers (if there's anything in particular that requires "deeper" interpretation). You are not required to post your answers for both, only one. Respond to other posts. As a group, we want you to all agree on final answers and what those answers mean (again, if there's any special meaning to the results you came up with).
Question 1.
The average retail prescription prices P (in dollars) from 1997 through 2004 can be approximated by the model P = 0.1220t2 + 1.529t + 18.72, 7 ≤ t ≤ 14, where t represents the year, with t = 7 corresponding to 1997. Answer the following, and discuss your results (are they reasonable/sensible?).
a) Determine algebraically when the average retail price was $40 and $50
b) According to the model, when will the average retail price reach $75?
c) Find the minimum average retail prescription price as predicted by the model and when that average price was reached.
Question 2.
The distance d (in miles) a car can travel on one tank of fuel is approximated by:
d = -0.024s2 + 1.455s + 431.5, 0 ≤ s ≤ 75, where s is the average speed of the car (in miles per hour). Answer the following, and discuss your results (are they reasonable/sensible?).
a) Determine algebraically the speeds at which the car could travel 400 miles and 500 miles on one tank of fuel.
b) According to the model, how fast would a person need to drive in order to travel 600 miles on one tank of fuel?
c) What is the maximum distance a person can travel on one tank of fuel and what speed yields that distance?