Name: Date: 2. Find the input of the function f() corresponding to the output f() t = 3to

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1 Name: Date: 1. Find the input of the function f( x) = 8 x+7 corresponding to the output f( x ) = 5.. Find the input of the function f() t = 48 corresponding to the output f() t = 3to t e +1 three decimal places. 3. Find the slope m and y-intercept b of the line whose equation is given below. 5 1 y = x 3 4. Find the rate of change of the function kt () = 0.6 t+.7million people of age t (in years). 5. Find the rate of change of the function r( p) = 13 p 1thousand dollars when p is hundreds of units sold. 6. For the function kr ( ) = 9.5 r 3.5, determine if the slope is positive or negative and if the function is increasing, decreasing, or constant. 7. For the function mr () = 8 r 9, determine the vertical axis intercept. 8. Residential customers who heat their homes with natural gas have their monthly bills calculated by adding a base service charge of $5.33 per month and an energy charge of cents per hundred cubic feet. Write an equation for the monthly charge y (in dollars) in terms of x, the number of hundreds of cubic feet used. 9. In a study using 50 foreign-language vocabulary words, the learning rate L (in words per minute) was found to depend on the number of words already learned x, according to the equation L= x. Use the intercepts to determine a window, and then use a graphing utility to graph the equation for x 0. Based on the graph, is the learning rate increasing or decreasing? Page 1

2 10. Graph the function y = 5(.5) x. 11. Graph the function. x y = 5( ) 1. Give the constant percentage change of the function Kr ( ) = 5(0.59) r 13. Give the constant percentage change for the function yx ( ) = 55.1(0.4) x x The monthly sales S for a product is given by S = 50, 000e, where x is the number of months that have passed since the end of a promotional campaign. How many months after the end of the campaign will sales drop below 000, if no new campaign is initiated? 15. An initial amount of 50 g of the radioactive isotope thorium-34 decays according to 0.088t Qt ( ) = 50e, where t is in years. How long does it take for half of the initial amount to disintegrate? This time is called the half-life of this isotope. 16. The purchasing power P (in dollars) of an annual amount of A dollars after t years of 9% inflation decays according to P = Ae 0.09t. Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 15 years? 17. The concentration y of a certain drug in the bloodstream t hours after an oral dosage 0.46 (with 0 t 15) is given by the equation y = 100(1 e t ). What is the concentration after 6 hours? 18. The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 003. Use a calculator to find the logistic function that models these data. Use x as the number of years past Year Percent with Internet Source: U.S. Department of Commerce Page

3 19. The following table gives the percent of the U.S. population with Internet connections for the years 1997 to 003. Use a calculator to find the logistic function that models these data and then use the model to predict when 58.8% of the U.S. population will have internet connections. Use x as the number of years past Year Percent with Internet Source: U.S. Department of Commerce 0. On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by 10,000 y = 0.99t e, where y is the total number infected at time t (in days). The school + will shut down if 55% of the students are ill. What value of t corresponds to this percentage? 1. In 1996, the population of a country was estimated at 4 million. For any subsequent year the population P( t) in millions is 40 () = 0.008t e P t where t is the number of years since Use a graphing calculator to estimate the population in Suppose the table below lists the cumulative number of bases stolen by a baseball player between 1951 and Estimate the number of bases this player stole in 1964 by using a logistic model for the data. Year Cumulative stolen bases Page 3

4 3. The table below models a population projection for a certain region for the years after Use a logistic model to estimate the population in 047. Year Population (millions) Year Population (millions) The sensitivity S to a drug is related to the dosage size by S = 150x x, where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. 5. Choose the function type for the mathematical model that best represents the given data set. x: f(x): Find the equation of the quadratic function that is the best fit for the given data. x y Suppose that the percent of total personal income that is used to pay personal taxes is given by y = 0.034x 0.044x+ 1.64, where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 17 percent. 8. If a ball is thrown upward at 18 feet per second from the top of a building that is 70 feet high, the height of the ball can be modeled by s = t 16t, where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 70 feet? Page 4

5 9. An equation that models the number of users of the Internet is y = x 14.14x+ 493 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 900 million users? 30. Choose the function type for the mathematical model that best represents the given data set. x: f(x): Page 5

6 Answer Key 1. x = 4. t = m =, b = slope is negative and function is decreasing y = x 9. decreasing % % months years 16. $70, yx ( ) = 0.585x e ,743, million 4. x = 0 milliliters, x =150 milliliters 5. quadratic 6. y =.04 x +.98 x t = 8 seconds cubic Page 6