The growth factor is 1/6. (II) The value changes from 1 to 1/6, a decrease of 5/6. The fractional change is -5/6; the percent change is - 83 1/3%. (III) Given: the initial value (when x=0) is 21.6. (IV) F(x) = 21.6(1/6)^x Note: Use the fractional form of the growth factor because it is exact; a decimal would only be an approximation. For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.B.4 Construct a function to model a linear relationship between two quantities.
x f ()x f ′()x gx() gx′() 1 6 4 2 5 2 9 2 3 1 3 10 – 4 4 2 4 –1 3 6 7 The functions f and g are differentiable for all real numbers, and g is strictly increasing. The table above gives values of the functions and their first derivatives at selected values of x. The function h is given by hx f gx() ()=−()6. Let Xbe a continuous random variable with pdf f(x) = 2(1 x);0 x 1. If Y = 2X 1 nd the pdf of Y. Example 4 Let Xbe a continuous random variable with pdf f(x) = 3 2 x2; 21 x 1. If Y = X nd the pdf of Y. 11
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