The following table gives the personal savings rate for sele

The following table gives the personal savings rate for selected years from 1980 to 2009. Personal Savings Savings Rate (%) -IYearl-Rate(%) Year a. Find a quadratic function that models the 3.29 3.48 3.87 personal savings rate as a function of the 2006 2008 2009 number of years after 1960. 2000 2002 b. Find and interpret the vertex of the graph of the rounded model from part (a) c. when after 1985 wel the personal savings rate reach a%? a. Determine the quadratic function that best fits the given data Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) b. Find the vertex of the graph of the rounded function obtained in part (a). Round the x-coordinate to the nearest tenth and the y-coordinate to the nearest thousandh The vertex is (Type an ordered pair.) Interpret the vertex of the graph of the function. Round the year to the nearest whole number In . the personal savings rate was c, when after 1985 will the personal savings rate reach 8%? (Round to the nearest year as needed.) (1) O minimum mean value O maximum O median value 9. Determine if the function is increasing or decreasing on the given interval. g(x) =-7x\":00) given function, g)-x is (1)on the interval (0,00). (1) decreasing increasing

Solution

g(x) = -7x^(2/3)

Deriivng :
g\'(x) = -14/3 * x^(-1/3)

= -14/(3x^(1/3))

Now, between (0,inf),
x^(1/3) is always positive

So, g\'(x) = -14/(3x^(1/3)) is aLWAYS negative

So, DECREASING -----> ANS

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