Analysis AB Name ______________________________________
U6D9 Applications Date _____________________ period __________
Solve each problem.
1. The number of deer P at any time t (in years) in a federal game reserve is given by
800 640
()
20 0.8
t
Pt
t
a. Find the number of deer when t is 15, 70, 100.
b. Find the horizontal asymptote of the graph of y = P(t).
c. Sketch a graph of the function.
d. According to the model, what is the largest possible deer population?
e. Write a paragraph that explains the parts of the graph in terms of the situation. What do
you know about the population? Are all parts of the graph valid for the model? Why or why
not?
2. Sunsport Recreation, Inc. wants to build a rectangular swimming pool with a pool surface
of 1200 square feet. They are required to have a walk of uniform width 2.5-ft surrounding the
pool. Let x be the length of one side of the swimming pool.
a. Draw a picture of the pool.
b. Express the area covered by the pool and sidewalk as a function of x.
c. Sketch a graph of the function,
d. Find the dimensions that cover the least area. (use your calculator if necessary)
3. Sarah rode her bike 10 miles from her home in Springfield, Illinois, and then took a 35-
mile trip by car to complete the trip from Springfield to Decatur. Assume the average rate of
the car was 40 mph faster than the average rate of the bike.
a. Express the total time t required to complete the 45-mile trip (bike and car) as a function
of the rate x of the car.
b. Use a graphical method to find the rate of the car if the total time of the trip was 1 hour.
Confirm your answer algebraically.
