College Algebra

The function P(x) = 80 - 30 log 2x models the percentage, P(x), of students who 100- could recall the important features of a classroom lecture as a function of time, S where x represents the number of days that have elapsed since the lecture was 80- given. The figure shows the graph of the function. After how many days do only 60- Percent two-fifths of the students recall the important features of the classroom lecture? (Let 40- P(x) = 40 and solve for x.) Locate the point on the graph that conveys this 20- information. Days The given bar graph shows the percentage of gross domestic product (GDP) in a state going toward health care from 2007 through 2010, Percentage of the Gross Domestic Product in the State with projections for 2014 and 2019. The data are modeled by the 21- 19.4 function f(x) = 1.5 In x + 15.1, where f(x) is the percentage of gross 18- 15.3 156 17.1 17.4 17.6 domestic product going toward health care x years after 2006. Use this 15- information to solve parts a and b. Percentage of GDP 2007 2008 2009 2010 2014 2019 a. Use the function to determine the percentage of gross domestic product that went toward health care in 2009. Does this underestimate or overestimate the percent displayed by the graph? By how much? Determine the percentage of gross domestic product that went toward health care in 2009 using the given function. b. According to the model, when will 20.1% of gross domestic product go toward health care