(a) What kinds of information would a modern historian need to determine the number of Africans involved in the slave trade?

(b) Why might a historian have trouble finding this information?

Textbooks usually give just the information that is needed to solve a problem. In real life, you must often sort through a greater amount of information and discard irrelevant facts, called red herrings. Find any red herrings in the following problem. Beneath the ocean surface, pressure changes at a rate of approximately 4.4 pounds per square inch for every 10-foot change in depth. A diver takes 30 minutes to ascend 25 feet from a depth of 150 feet. What change in pressure does the diver experience?

The title of the graph does not provide much information about the contents of the graph. What additional information would be useful to better understand and use this graph?

An initial population $P_0$ is given along with a renewal rate $R(t)$ and a survival function $S(t)$. In each case, use the given information to find the population at the end of the indicated term $T$.

$P_0=100,000 ; R(t)=90 e^{0.1 t} ; S(t)=e^{-0.2 t} ; t$ in years; term $T=10$ years

An initial population $P_0$ is given along with a renewal rate $R(t)$ and a survival function $S(t)$. In each case, use the given information to find the population at the end of the indicated term $T$.

$P_0=200,000 ; R(t)=50 e^{0.12 t} ; S(t)=e^{-0.017 t} ; t$ in hours; term $T=20$ hours

In data communication, messages are usually combinations of characters, and each character consists of a number of bits. A bit is the smallest unit of information and is either 1 or 0 . Suppose that L, the length of a character (in bits) is a geometric random variable with parameter p. If a sender emits messages at the rate of 1000 bits per second, what is the distribution of T, the time it takes the sender to emit a character?

On the first day of each month, the manager of a small company estimates the rate at which profit is expected to increase during that month. The results are listed in the accompanying table for the first 6 months of the year, where $P^{\prime}(t)$ is the rate of profit growth in thousands of dollars per month expected during the $t$ th month ( $t=1$ for January, $t=6$ for June). Use this information together with the trapezoidal rule to estimate the total profit earned by the company during this 6-month period (January through June).

Consider the following information. You are on a canoe trip. You can paddle your canoe at a rate of $x+2$ miles per hour downstream and $x-2$ miles per hour upstream. You travel 15 miles downstream and 15 miles back upstream.

$\bull$ Write an expression for the travel time downstream and an expression for the travel time upstream.

The table below lists the U.S. cities with populations over 100,000 that had the highest number of violent crimes per 1000 residents per year. The violent crimes include murder, rape, aggravated assault, and robbery.

a. Which city has the highest rate of violent crimes?

b. The population of Baltimore is approximately 703,000. Estimate the number of violent crimes committed in that city. Round to the nearest whole number.

An initial population $P_0$ is given along with a renewal rate R(t) and a survival function S(t). Use the given information to find the population at the end of the indicated term T. $P_{0}=200,000; R(t)=50 e^{0.12t}; S(t)=e^{-0.017 t};$ t in hours; term T = 20 hours

Using information from the utility bills for the coldest month last year, estimate the average rate of heat loss from your house for that month. In your analysis, consider the contribution of the internal heat sources such as people, lights, and appliances. Identify the primary sources of heat loss from your house and propose ways of improving the energy efficiency of your house.

presents selected information from the notes to the financial statements of Catiman Limited, a manufacturer of farming equipment, for the years ending October 31, 2013, 2012, and 2011. Catiman applies U.S. GAAP. d. Catiman combines the effect of nondeductible costs and other items in its income tax reconciliation. Will nondeductible costs have the effect of increasing or decreasing the effective tax rate? Explain.

The price of a movie ticket averages $10.25 and is increasing by 3% per year. Use that information to complete parts (a) through (c) below. a. What is the multiplier in this situation? b. Write a function that represents the cost of a movie ticket n years from now. c. If tickets continue to increase at the same rate, what will they cost 10 years from now?

[Related to the Apply the Concept on page 270] An opinion columnist for bloomberg.com observed, “A lot of people seem to think that committed, long-term shareholders should get more say than those who can bail out at any moment.”

Is there a good argument against giving long-term shareholders more say in running a corporation? Briefly explain.