Use the General Power Rule where appropriate to find the derivative of the following functions. f(x)=

$$2^x$$

What do the x- and y-intercepts of your graph represent?

Use Cramer's Rule to solve each system of equations.

$$\left. \begin{array} { l } { - 8 a - 5 b = - 27 } \\ { 7 a + 6 b = 22 } \end{array} \right.$$

The cost of crude oil increases by 25 percent. Crude oil is the raw material used to produce plastic. What will this do to the supply curve for plastic toys?

Is the following sentence true or false? The solubility of sodium chloride in water increases to 39.2 g per 100 g of water at

$$100 ^ { \circ } \mathrm { C }$$

from 36.2 per 100 g of water at

$$25 ^ { \circ } \mathrm { C }$$

.

Solve the equation. Check your solution. -3 = z/(6 + 11)

Identify the asymptotes, domain, and range of the function.

$$f ( x ) = \frac { 3 } { x + 2 } + 1$$

Find the common difference of each arithmetic sequence. Then find the next term. 4, x + 4, 2x + 4, 3x + 4, ....

Determine whether the following statements are true and give an explanation or counterexample. If p(x) is the Taylor series for f centered at 0, then p(x-1) is the Taylor series for f centered at 1.

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

$$a = 63 , b = 22 , c = 50$$

Which measures the average kinetic energy of air molecules? A. humidity B. pressure C. speed D. temperature

What alcohols are obtained from the reduction of the following compounds with sodium borohydride? a. 2-methylpropanal, b. cyclohexanone, c. 4-tert-butylcyclohexanone, d. acetophenone

In December 2011, Consumer Reports published their study of labeling of seafood sold in New York, New Jersey, and Connecticut. They purchased 190 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pieces to standard gene fragments that can identify the species. Laboratory results indicated that 22% of these packages of seafood were mislabeled, incompletely labeled, or misidentified by store or restaurant employees. a) Construct a 95% confidence interval for the proportion of all seafood packages in those three states that are mislabeled or misidentified. b) Explain what your confidence interval says about seafood sold in these three states. c) A 2009 report by the Government Accountability Board says that the Food and Drug Administration has spent very little time recently looking for seafood fraud. Suppose an official said, "That's only 190 packages out of the billions of pieces of seafood sold in a year. With the small number tested, I don't know that one would want to change one's buying habits." (An official was quoted similarly in a different but similar context). Is this argument valid? Explain.

Determine whether the equation represents a linear or nonlinear function. Explain.

$$y = \sqrt [ 3 ] { 8 } - x$$