a. Show that the logistic function $f(x)=\frac{N}{1+A b^{-x}}$ can be written in the form $f(x)=\frac{N b^{x}}{A+b^{x}}$. b. Use the result of part (a) and a suitable substitution to show that $\int \frac{N}{1+A b^{-x}} d x=\frac{N \ln \left(A+b^{x}\right)}{\ln b}+C$. The rate of graduation of private high school students in the United States for the period 1994-2008 was approximately $r(t)=220+\frac{110}{1+3.8(1.27)^{-t}}$ thousand students per year $(0 \leq t \leq 14)$ t years since 1994. Use the result of part (b) to estimate the total number of private high school graduates over the period 2000-2008.

Indicate whether each of the following types of transactions will either decrease owner’s equity:

1. owner’s investments
2. revenues
3. expenses
4. owner’s withdrawals

a. Return on assets, or ROA, can be expressed as the product of two ratios. Which two?\

b. Return on equity, or ROE, can be expressed as the product of three ratios. Which three?

Palencia Paints Corporation has a target capital structure of 35% debt and 65% common equity, with no preferred stock. Its before-tax cost of debt is 8%, and its marginal tax rate is 40%. The current stock price is $\mathrm{P}_{0}=\$ 22.00$. The last dividend was $\mathrm{D}_{0}=\$ 2.25$, and it is expected to grow at a 5% constant rate. What is its cost of common equity and its WACC?

This period, Amadeus Co. purchased its only available-for-sale investment in the notes of Bach Co. for $83,000. The period-end fair value of these notes is$84,500. Amadeus records a

• a. Credit to Unrealized Gain—Equity for $1,500.
• b. Debit to Unrealized Loss—Equity for$1,500.
• c. Debit to Investment Revenue for $1,500.
• d. Credit to Fair Value Adjustment—Available-for-Sale for$3,500.
• e. Credit to Cash for $1,500.

Indicate whether each of the following types of transactions will either increase owner’s equity.

1. owner’s investments
2. revenues
3. expenses
4. owner’s withdrawals

For the fiscal year, sales were $191,350,000 and the cost of merchandise sold was$114,800,000.

a. What was the amount of gross profit?
b. If total operating expenses were $18,250,000, could you determine net income?
c. Is Customer Refunds Payable an asset, liability, or owner’s equity account, and what is its normal balance?
d. Is Estimated Returns Inventory an asset, liability, or owner’s equity account, and what is its normal balance?

Assume the definition of class bagType as given in previous Exercise. Answer the following questions: a. Write the definition of the member function set so that private members are set according to the parameters. b. Write the definition of the member function print that prints the values of the data members. c. Write the definition of the default constructor of the class bagType so that the private member variables are initialized to "", 0.0, 0.0, 0.0, 0.0, respectively. d. Write a C++ statement that prints the value of the object newBag. e. Write a C++ statement that declares the object tempBag of type bagType, and initializes the member variables of tempBag to "backPack", 15, 8, 20, and 49.99, respectively.

Refer to Samsung’s 2013 balance sheet in Appendix A near the end of the book. Confirm that its total assets equal its total liabilities plus total equity.

The following information was taken from Charu Company's balance sheet:

$$\begin{array}{lr}\text { Fixed assets (net) } & \$ 860,000 \\ \text { Long-term liabilities } & 200,000 \\ \text { Total liabilities } & 600,000 \\ \text { Total stockholders' equity } & 250,000\end{array}$$

Determine the company's (a) ratio of fixed assets to long-term liabilities and (b) ratio of liabilities to stockholders' equity. Round to one decimal place.

In early $2015$, Abercrombie & Fitch (ANF) had a book equity of $\$ 1390$ million, a price per share of $\$ 25.52$, and $69.35$ million shares outstanding. At the same time, The Gap (GPS) had a book equity of $\$ 2983$ million, a share price of $\$ 41.19$, and $421$ million shares outstanding.

a. What is the market-to-book ratio of each of these clothing retailers?

b. What conclusions can you draw by comparing the two ratios?

Design a class named Account that contains: - A private int data field named id for the account (default 0). - A private double data field named balance for the account (default 0). - A private double data field named annualInterestRate that stores the current interest rate (default 0). Assume all accounts have the same interest rate. - A private Date data field named dateCreated that stores the date when the account was created. - A no-arg constructor that creates a default account. - A constructor that creates an account with the specified id and initial balance. - The accessor and mutator methods for id, balance, and annualInterestRate. - The accessor method for dateCreated. - A method named getMonthlyInterestRate() that returns the monthly interest rate. - A method named getMonthlyInterest() that returns the monthly interest. - A method named withdraw that withdraws a specified amount from the account. - A method named deposit that deposits a specified amount to the account. Draw the UML diagram for the class and then implement the class. (Hint: The method getMonthlyInterest() is to return monthly interest, not the interest rate. Monthly interest is balance * monthlyInterestRate. monthlyInterestRate is annualInterestRate / 12. Note that annualInterestRate is a percentage, e.g., like 4.5%. You need to divide it by 100.) Write a test program that creates an Account object with an account ID of 1122, a balance of $20,000, and an annual interest rate of 4.5%. Use the withdraw method to withdraw$2,500, use the deposit method to deposit $3,000, and print the balance, the monthly interest, and the date when this account was created.

Determine the financial statement on which the item below appears. Use I for income statement. E for statement of owner's equity, and B for balance sheet.
 Owner Withdrawals

Determine the financial statement on which the item below appears. Use I for income statement. E for statement of owner's equity, and B for balance sheet.
 Services Revenue