Exam 2: Quadratic and Other Special Functions

The graph of the profit function is given as follows. Consider the average rate of change of the profit from a to 400 where a lies to the left of 400. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 400? ​ ​

The profit function for a certain commodity is . Find the level of production that yields maximum profit, and find the maximum profit. ​

An equation that models the number of users of the Internet is million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users? ​

Find the exact real solutions to the equation, if they exist. ​ ​

The demand function for a product is given by , where x is the number of units and p is the price in dollars. Graph this demand function for , with x on the horizontal axis. ​

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. ​ ​

A fissure in the earth appeared after an earthquake. To measure its vertical depth, a stone was dropped into it, and the sound of the stone's impact was heard 3.3 seconds later. The distance (in feet) the stone fell is given by , and the distance (in feet) the sound traveled is given by . In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places. ​

The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. ​

Assume that sales revenues, in millions, for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places. ​

Factor the function . ​

Sketch the graph of the following function. ​ ​

By recognizing shapes and features of polynomial functions, sketch the graph of the function . Use a graphing utility to confirm your graph. ​

The table that follows gives the population of a city. Find the power function that best fits the data, with x equal to the number of years past 1950. According to the model, will the city's population be greater than 1,400 by the year 2010? Round your final answer to three decimal places.

Find the exact real solutions of the equation , if they exist. ​

If total costs are and total revenues are , find the break-even points. ​

Find the equation of the quadratic function that is the best fit for the given data. Round your final values to two decimal places. ​

Solve the equation by first multiplying by the LCD, and then solving the resulting equation. ​

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points and any asymptotes. ​ ​

The time t, in seconds, that it takes a 2005 Corvette to accelerate to x mph can be described by . How fast is the Corvette going after 9.08 seconds? Give your answer to the nearest tenth. ​

Use a graphing calculator to graph the profit function . ​