Reminder Round all answers to two decimal places unless otherwise indicated.
Zipf’s Law The linguist George Kingsley Zipf (1902-1930) proposed a law that bears his name. In a typical English text, the most commonly occurring word is "the." We say that its frequency rank r is 1. The frequency
where
a. Use the frequency information given for "the" to determine the value of r
b. The third most common English word is "and." According to Zipf's law, what is the frequency of this word in a typical English text? Round your answer to one decimal place.
c. If one word's frequency rank is twice that of another, how do their frequencies of occurrence compare?
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Chapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Mortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forwardDepreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forward
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runners time at the end of each lap, obtaining the data in the following table. aWhat was the mans average speed rate between 68 s and 152 s? bWhat was the mans average speed between 263 s and 412 s? cCalculate the mans speed for each lap. Is he slowing down, speeding up or neither? Time s Distance m 32 200 68 400 108 600 152 800 203 1000 263 1200 335 1400 412 1600arrow_forwardThe Kelvin Temperature Scale Physicists and chemists often use the Kelvin temperature scale. In order to determine the relationship between the Fahrenheit and Kelvin temperature scales, a lab assistant put Fahrenheit and Kelvin thermometers side by side and took readings at various temperatures. The following data were recorded. K = kelvins F = degrees Fahrenheit 200 -99.67 220 -63.67 240 -27.67 260 8.33 280 44.33 300 80.33 a. Show that the temperature F in degrees Fahrenheit is a linear function of the temperature K in kelvins. b. What is the slope of this linear function? Note: Be sure to take into account that the table lists kelvins in jumps of 20 rather than in jumps of 1. c. Find a formula for the linear function. d. Normal body temperature is 98.6 degrees Fahrenheit. What is that temperature in kelvins? e. If temperature increases by 1 kelvin, by how many degrees Fahrenheit does it increase? If temperature increases by 1 degree Fahrenheit, by how many kelvins does it increase? f. The temperature of 0 kelvins is known as absolute zero. It is not quite accurate to say that all molecular motion ceases at absolute zero, but at that temperature the system has its minimum possible total energy. It is thought that absolute zero cannot be attained experimentally, although temperatures lower than 0.0000001 kelvin have been attained. Find the temperature of absolute zero in degrees Fahrenheit.arrow_forwardHeart Disease In a certain country, the number of deaths due to heart disease decreased from 235 in one year to 221 in the next year. What percentage decrease in deaths due to heart disease does this represent?arrow_forward
- The Decibel scale Exercise S-7 through S-10 refer to the decibel scale. If one sound has a relative intensity one-tenth that of another, how do their decibel levels compare?arrow_forwardKeplers Third Law According to Keplers third law of planetary motion, the mean distance D, in millions of miles, from a planet in our solar system to the sun is related to the time P, in years, that it takes for the planet to complete a revolution around the sun, and the relationship is D=93P2/3. It takes the planet Pluto 249 years to complete a revolution around the sun. What is the mean distance from Pluto to the sun? What is the mean distance from Earth to the sun? Give your answers to the nearest million miles.arrow_forwardpH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?arrow_forward
- Draw a scatter plot for the data in Table 3. If we wanted to know when the population would reach 15,000,would the answer involve interpolation or extrapolation?arrow_forwardSpeed of Sound in the North Atlantic The speed of sound in ocean water is 1148.94meterspersecond, provided that the ocean water has a salinity of 35 35partsperthousand, the temperature it 0degreesCelsius, and the measurement is taken at the surface. If any one of these three factors varies, the speed of sound also changes. Different oceans often differ in salinity. In the North Atlantic Central Water the main body of water for the northern half of the Atlantic Ocean, the salinity can be determined from the temperature, so the speed of sound depends only on temperature and depth. A simplified polynomial formula for velocity in this body of water is V=1447.733+4.7713T0.05435T2+0.0002374T3+0.0163D+1.675107D27.1391013TD3 Here V is the speed of sound in meters per second, T is the water temperature in degrees Celsius, and D is depth in meters. This formula is valid for depths up to 8000 meters and for temperatures between 0 and 30 degrees Celsius. a. What type of polynomial is V as a function of T alone? Of D alone? b. For a fixed depth of 1000meters, write the formula for V in terms of T alone. c. Graph V as a function of T for the fixed depth of 1000meters. d. What is the concavity of the graph from part c? What does this imply about the speed of sound at that depth as temperature increases?arrow_forwardHarris-Benedict Formula Your basal metabolic rate is the amount of energy in calories your body needs to function at rest. The Harris-Benedict formula is used to estimate the basal metabolic rate. There is one formula for adult males and another for adult females. In these formulas, w is your body weight in pounds, h is your height in inches, a is your age in years, M=M(w,h,a) is the basal metabolic rate for adult males, and F=(w,h,a) is the basal metabolic rate for adult females: M=66+6.3w+12.7h6.8aF=655+4.3w+4.7h4.7a Use functional notation to express your own basal metabolic rate, and then calculate its value.arrow_forward
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