Superlesson
Project 8-2
Advanced Algebra
Chapter 8, Polynomials and Polynomial Functions
Polynomials can be used to model some natural phenomena. Associated polynomial equations can be solved to find optimal solutions to problems relating to the phenonomena.
Part A, Solving Polynomial Equations by Graphing;
Part B, Factors and Roots of Polynomials
1. Grunion are fish that come ashore briefly to lay their eggs in the sand.
a. When do grunion lay their eggs?
b. The polynomial function h = 0.0002 t4 0.003 t 3 0.09 t2 + t + 9 approximates the wave height h in feet at one coastal location at time t on August 19, 1998 for the 24-hour interval from t = 0, to t = 24. Graph the function in the indicated interval.
c. Suppose a decision is made to rope off the beach when the grunion are expected to come ashore, in order to protect the fish laying eggs. At what time will the grunion be arriving? About how high will the waves be?
Part C, The Fundamental Theorem;
Part D, Making Connections
2. A builder wondered if a 25-ft white pine log will produce enough lumber to build an entire house.
a. Large quantities of lumber are measured in board-feet. One board foot bf is the amount of lumber in a 12-in. square board that is 1-in. thick. About how many board feet of lumber would you need to build a 1500 ft2 house?
b. Find the normal range of heights and diameters of white pines.
c. The Doyle Log Rule gives the approximate lumber yield, y of a log bf given the radius r (in.) and length L (ft) of the log:
The builder's white pine log was 25-ft long and had a uniform diameter over its entire length. Use the length of the log and the number of board feet in a 1500 ft2 house to write a quadratic equation you can solve to find the radius that the tree must have if it is to supply all the lumber or the house.
d. Solve the equation for r by factoring.
e. Will a 25-ft white pine log of normal radius supply enough lumber for the house?
