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The table shows the total (cumulative) number of ebola cases reported in Sierra Leone during a serious West African ebola outbreak in \(2014-2015 .\) The total number of cases is reported \(x\) months after the start of the outbreak in May \(2014 .\) $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Months after } \\ \text { May 2014 } \end{array} & \text { Total Ebola Cases } \\ \hline 0 & 16 \\ 2 & 533 \\ 4 & 2021 \\ 6 & 7109 \\ 8 & 10,518 \\ 10 & 11,841 \\ 12 & 12,706 \\ 14 & 13,290 \\ 16 & 13,823 \\ 18 & 14,122 \\ \hline \end{array} $$ (a) Use the regression feature of a calculator to determine the quadratic function that best fits the data. Let \(x\) represent the number of months after May \(2014,\) and let \(y\) represent the total number of ebola cases. Give coefficients to the nearest hundredth. (b) Repeat part (a) for a cubic function (degree 3). Give coefficients to the nearest hundredth. (c) Repeat part (a) for a quartic function (degree 4). Give coefficients to the nearest hundredth. (d) Compare the correlation coefficient \(R^{2}\) for the three functions in parts (a)-(c) to determine which function best fits the data. Give its value to the nearest ten-thousandth.

A rectangular piece of cardboard measuring 12 in. by 18 in. is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let \(x\) represent the length of a side of each such square in inches. Give approximations to the nearest hundredth. (a) Give the restrictions on \(x\). (b) Determine a function \(V\) that gives the volume of the box as a function of \(x\). (c) For what value of \(x\) will the volume be a maximum? What is this maximum volume? (Hint: Use the function of a graphing calculator that enables us to determine a maximum point within a given interval.) (d) For what values of \(x\) will the volume be greater than 80 in. \(^{3}\) ?

A certain right triangle has area 84 in. \({ }^{2}\) One leg of the triangle measures 1 in. less than the hypotenuse. Let \(x\) represent the length of the hypotenuse. (a) Express the length of the leg mentioned above in terms of \(x\) (b) Express the length of the other leg in terms of \(x\). (c) Write an equation based on the information determined thus far. Square each side and then write the equation with one side as a polynomial with integer coefficients, in descending powers, and the other side equal to \(0 .\) (d) Solve the equation in part (c) graphically. Find the lengths of the three sides of the triangle.

Determine whether each polynomial function is even, odd, or neither. \(f(x)=2 x^{3}\)

Determine whether each polynomial function is even, odd, or neither. \(f(x)=4 x^{5}-x^{4}\)