Sales of a product, under relatively stable market conditions but in the absence of promotional activities such as advertising, tend to decline at a constant yearly rate. This rate of sales decline varies considerably from product to product, but it seems to remain the same for any particular product. The sales decline can be expressed by the function $S(t)=S_{0} e^{-a t}$, where S(t) is the rate of sales at time t measured in years, $S_0$ is the rate of sales at time t=0, and a is the sales decay constant. (a) Suppose the sales decay constant for a particular product is a=0.10. Let $S_0$=50.000 and find S(1) and S(3) to the nearest thousand. (b) Find S(2) and S(10) to the nearest thousand if $S_0$=80.000 and a=0.05.

Does the given differential equation model unlimited growth, exponential decay, limited growth, or logistic growth? $y^{\prime}=-0.0152 y$

Determine the domain and range in interval or algebraic form.

Does the manager of a Samsung distribution center participate in longterm budgeting? Explain.

Zinc hydroxide is an amphoteric substance. Write equations that describe $\mathrm{Zn}(\mathrm{OH})_{2}$ acting as a Bronsted-Lowry base toward $\mathrm{H}^{+}$ and as a Lewis acid toward $\mathrm{OH}^{-}.$

Bright Day Company produces two beverages, Hi-Voltage and EasySlim. Data about these products follow.

$$\begin{matrix} & \text{Hi-Voltage} & \text{EasySlim}\\ \text{Production volume} \ldots\ldots\ldots & \text{12,500 bottles} & \text{180,000 bottles}\\ \text{Liquid materials}\ldots\ldots\ldots & \text{1,400 gallons} & \text{37,000 gallons}\\ \text{Dry materials} \ldots\ldots\ldots & \text{620 pounds} & \text{12,000 pounds}\\ \text{Bottles} \ldots\ldots\ldots & \text{12,500 bottles} & \text{180,000 bottles}\\ \text{Labels}\ldots\ldots\ldots & \text{3 labels per bottle} & \text{1 label per bottle}\\ \text{Machine setups} \ldots\ldots\ldots & \text{500 setups} & \text{300 setups}\\ \text{Machine hours}\ldots\ldots\ldots & \text{200 MH} & \text{3,750 MH}\\ \end{matrix}$$

Additional data from its two production departments follow.

$$\begin{matrix} \text{Department} & \text{Driver} & \text{Cost}\\ \text{Mixing department}\\ \text{Liquid materials} \ldots\ldots\ldots & \text{Gallons} & \text{\$ 2,304}\\ \text{Dry materials} \ldots\ldots\ldots & \text{Pounds} & \text{6,941}\\ \text{Utilities}\ldots\ldots\ldots & \text{Machine hours} & \text{1,422}\\ \text{Bottling department}\\ \text{Bottles} \ldots\ldots\ldots & \text{Units} & \text{\$77,000}\\ \text{Labeling}\ldots\ldots\ldots & \text{Labels per bottle} & \text{6,525}\\ \text{Machine setup} \ldots\ldots\ldots & \text{Setups} & \text{20,000}\\ \end{matrix}$$

1. Determine the cost of each product line using ABC. 2. What is the cost per bottle of Hi-Voltage? What is the cost per bottle of EasySlim? 3. If Hi-Voltage sells for $3.75 per bottle, how much profit does the company earn per bottle of Hi-Voltage that it sells? 4. What is the minimum price that the company should set per bottle of EasySlim? Explain.

Carbon monoxide (CO) forms bonds to a variety of metals and metal ions. Its ability to bond to iron in hemoglobin is the reason that CO is so toxic. The bond carbon monoxide forms to metals is through the carbon atom:

$$\mathrm{M}-\mathrm{C} \equiv \mathrm{O}$$

Assign formal charges to the atoms in CO. Which atom would you expect to bond to a metal on this basis?

Carbon tetrachloride, $\mathrm{CCl}_{4},$ has a vapor pressure of 213 torr at $40 .^{\circ} \mathrm{C}$ and 836 torr at $80 .^{\circ} \mathrm{C}.$ What is the normal boiling point of $\mathrm{CCl}_{4} ?$

Explain the difference between melting and melting point.

In the hybrid orbital model, compare and contrast $\sigma$ bonds with $\pi$ bonds. What orbitals form the $\sigma$ bonds and what orbitals form the $\pi$ bonds? Assume the z-axis is the internuclear axis.

Find $f^{\prime}(x)$ and simplify. $f(x)=\frac{2 x}{1+\ln x}$

How are boiling water and electrolysis different?

Using the methods of this section: (a) Find the first few terms of the Maclaurin series for each of the following functions. (b) Find the general term and write the series in summation form. (c) Check your results in (a) by computer. (d) Use a computer to plot the function and several approximating partial sums of the series. $\ln \frac{1+x}{1-x}$

Solve for the variable without using a calculator. $y=\ln (\ln e)$