The table lists the Consumer Price Index for all U.S. urban consumers (CPI-U) with 1982-1984 = 100 for selected years between 1960 and 2008 Consumer Price Index for All U.S. Urban Consumers 1982-1984 = 100 Year CPI-U, C 1960 29.6 1970 38.8 82.4 1980 1990 130.7 2000 172.2 2005 195.3 2008 215.3 (a) Align the input data to the number of years since 1960. Which model type other than quadratic might be considered when modeling this data? Why? OThe increasing, concave up scatter plot of this data suggests a quadratic or an logarithmic function OThe increasing, concave up scatter plot of this data suggests a quadratic or an exponential function OThe increasing, concave down scatter plot of this data suggests a quadratic or an logarithmic function. this data suggests a quadratic or an exponential function O The increasing, concave down scatter plot (b) Use the end behavior to choose the better model O quadratic logarithmic exponential Write the function for the better model that gives the CPI (based on a CPI = 100 for 1982-1984) for all U.S. urban consumers, where t is the number of years since 1960, with data from 0 st s 48. (Round all numerical values to three decimal places.) C() 0.0385x 1 2.1462x 24.089 x
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
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In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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