Exam 11: Polynomial and Rational Functions

The volume of pollutants (in millions of cubic feet) in a certain reservoir is given by ^{P(t)=360 + 35t} , where t is time in years. The volume of the reservoir (including pollutants) is gradually increasing and is given by ^{R(t) = 14,000+ 110t}. Let ^C(t) be the fraction of the reservoir's volume that consists of pollutants. If these trends continue for many years, approximately what percent of the reservoir's total volume would eventually be pollutants? Round to 1 decimal place.

George measures the force exerted by a certain spring when it is stretched various distances beyond its natural length. The data he gathers is compiled in the following table. - He wishes to describe the force as a function of the stretched distance, and decides to use an exponential function model. After fitting an exponential function to the data, he uses it to estimate the force when the spring is stretched 21 inches. What is his approximation (to three decimal places) of this force?

The power function through the point (1, 3) and (3, 5) is , where k = _____ and p = _____. Round the second answer to 3 decimal places.

Let . Which of the following statements are true?

Let and be graphed in the following figure. Which of the following is true?

List the zeros of the function in ascending order, separated by commas.

The squirrel population in a certain area is estimated each year and recorded in the table below. Suppose the squirrel population in a given year is a function of the number of years since 1998. -Fit a quadratic function to the data and use it to estimate the squirrel population (rounded to the nearest whole number) in 2012.

Write the equation for the following graph: The graph of shifted to the left 4 units and up 1 units.

Farmer Brown has 117 feet of fence. He wishes to close in a rectangular field using the barn as one side of the field. Suppose each side of the field perpendicular to the barn has length feet. What is the area of the fenced in field?

Can be written in the form of an exponential function, a power function, or neither?

According to one advertisement, Burger King's all-beef hamburger patties have 85 % more beef than McDonald's all-beef hamburger patties. If both chains serve circular patties of the same thickness, then the diameter of Burger King's patties,d_B , will be directly proportional to the diameter of McDonald's patties, d_M . Which of the following formulas express d_M as a function of d_B ?

If and , then on the interval _____ < x < _____.

Use a graphing calculator to find all the real zeros of . List them in ascending order, separated by commas.

The volume of pollutants (in millions of cubic feet) in a certain reservoir is given by P(t)=300 + 30t , where t is time in years. The volume of the reservoir (including pollutants) is gradually increasing and is given by ^{R(t) = 14,000+ 130t} . Let ^C(t) be the fraction of the reservoir's volume that consists of pollutants. What percent of the reservoir's total volume consisted of pollutants in the year t = 0? Round to 1 decimal place.

Describe the graph of .

A polynomial with integer coefficients having as a zero is , where a = _____, b = _____, and c = _____. Make your value for a be positive and as small as possible.

The following table represents the amount of monthly data handled by an Internet server, sampled at six month intervals for the years 1993-1995. Let d be the number of data packets handled monthly (in billions), and t be time in years since December, 1992. The best exponential model for this data is of the form , where a = _____ and b = _____. Give both answers to 6 decimal places.

Which of the following could represent a complete graph of where a is a constant?

Suppose y is inversely proportional to x. If y = 1 when x = 6, what is the value of x when y is 2?