FST Chapter 2 ReviewName:

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  1. Consider the function f(x) = –9.8x2 - 5.2x + 12.7.
  2. Evaluate f(2) to the nearest tenth.
  1. Find the value(s) of x such that f(x) = -503.9
  1. Find the domain of f(x).
  1. Find the range of f(x).
  1. Evaluate g(2n) if g(x) = 5x2 - 3.
  1. Use the following graphs to answer the questions below.
  1. Which scatterplots indicate a negative association between variables?
  1. Which scatterplots indicate a correlation coefficient close to zero?
  1. Which correlation coefficient(s) equal 1?
  1. The equation P = 3,424,000(1.013)xcan be used to model the population P of New Zealand x years after 1993. In 2008, this model produced a residual of 17,000 rounded to the nearest thousand. What was the actual population in 2008?
  1. Stephen and Chris fi t different lines to a scatterplot by eye. The sum of squared residuals was 34 for Stephen’s line and was 576 for Chris’s line. Use the sum of squared residuals to explain which of their models is a better fit to the data.
  1. Suppose a ball is thrown upward at a velocity of 44 from a cliff 200 feet above a dry riverbed. Use the formula h = – ½ gt2 + v0t + h0 where g = 32 .
  2. Write an equation for the height h (in feet above the riverbed) of the ball after t seconds.
  1. What is the height of the ball 3 seconds after it is thrown?
  1. At what time will the ball hit the riverbed?
  1. Suppose that y = 60 when x = 10 and y varies inversely as x.
  2. Compute the constant of variation.
  1. Find y when x = 3. 8.
  1. Does the function f with f(x) = 105(1.2)xmodel exponential decay or exponential growth? How do you know?
  1. A movie studio uses the regression equation y = 2.51x + 471.10 to predict how much money a movie will earn based on the cost of making the movie. Here, y = world revenues in millions of dollars and x = the movie’s budget in millions of dollars. The movie “Regression without a Cause” had a budget of $115 million and earned $524 million. What is the residual?
  1. Cesium-137 has a half-life of 30 years. How much of a 10-gram sample will be left after 20 years?
  1. The residuals for a linear and inverse-square model are graphed below. What do these graphs tell you about the appropriateness of each model?
  1. The table below shows the height h in feet of a ball above ground level t seconds after being thrown off the top of a building.
  1. Fit a quadratic model to the data.
  1. Is this a theory-based model or is it an impressionistic model?
  1. From your model, what is the height of the ball 4 seconds after it was thrown?
  1. The table at the right lists the percent of U.S. citizens aged 18–24 who voted in midterm elections from 1974 to 2002.
  1. Using the line of best fi t with the number of years after 1974 as the independent variable, what does the slope tell you about voter turnout in midterm elections among 18–24 year olds?
  1. Find the correlation coefficient. What does the correlation coefficient tell you about the relationship between the year and voter turnout in midterm elections among 18–24 year olds?
  1. Sonia researched the number of fast-food restaurants in her city in several years and recorded the data in the table below.
  1. Make a scatterplot of the data. Which model appears appropriate for the data?
  1. Plot the residuals for the regression equations for various models.
  1. Write a sentence or two explaining your choice of best fit model.
  1. Identify the independent and dependent variables: The number of pizzas ordered is determined by the number of people at the party.
  1. In June 2008, Greg purchased a $50 U.S. EE Savings Bond for $32.86. EE Bonds are an accrual-type security, which means that interest is added to the bond monthly and is paid when you cash in the bond for its face value at maturity. The bonds had a 1.4% annual interest rate when Greg purchased them.
  2. Express the value of the bond A as a function of n, the number of months after June, 2008.
  1. Use a calculator and the equation found in Part a to estimate the number of months for the bond to reach maturity.
  1. The half-life of one isotope of the synthetic element Fermium (255Fm) is 20 hours.
  2. How many hours are there in three half-life periods?
  1. How much of an 8-gram sample of 255Fm will be left after three half-life periods?
  1. Find an equation that models the decay of an 8-gram sample of 255Fm.
  1. Use the equation found in Part c to determine how much of an 8-gram sample will be left after 150 hours.