Problem 1E: The cost, C (in dollars), to produce g gallons of a chemical can be expressed as C = f(g). Using... Problem 2E: The time for a chemical reaction, T (in minutes), is a function of the amount of catalyst present, a... Problem 3E: The temperature, T, in degrees Fahrenheit, of a cold yam placed in a hot oven is given by T = f(t),... Problem 4E: The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by... Problem 5E: The cost, C (in dollars), to produce q quarts of ice cream is C = f(q). In each of the following... Problem 6E: An economist is interested in how the price of a certain item affects its sales. At a price of p, a... Problem 7E: Let S(t) be the amount of water, measured in acre-feet,7 that is stored in a reservoir in week t.... Problem 8E: The wind speed, W, in meters per second, at a distance x km from the center of a hurricane is given... Problem 9E: Suppose C(r) is the total cost of paying off a car loan borrowed at an annual interest rate of r%.... Problem 10E: Let f(x) be the elevation in feet of the Mississippi River x miles from its source. What are the... Problem 11E: In Exercises 1115, give the units and sign of the derivative. h(t), where h(t) is the altitude of a... Problem 12E: In Exercises 1115, give the units and sign of the derivative. f(t), where f(t) is the temperature of... Problem 13E: In Exercises 1115, give the units and sign of the derivative. P(r), where P(r) is the monthly... Problem 14E: In Exercises 1115, give the units and sign of the derivative. T(v), where T(v) is the time, in... Problem 15E: In Exercises 1115, give the units and sign of the derivative. W(x), where W(x) is the work required,... Problem 16E: Suppose P(t) is the monthly payment, in dollars, on a mortgage which will take t years to pay off.... Problem 17E: After investing 1000 at an annual interest rate of 2% compounded continuously for t years, your... Problem 18E: Investing 1000 at an annual interest rate of r%, compounded continuously, for 10 years gives you a... Problem 19E: Meteorologists define the temperature lapse rate to be dT/dz where T is the air temperature in... Problem 20E: Let dVdrr=2=16. (a) For small r, write an approximate equation relating V and r near r = 2. (b)... Problem 21E: Let R = f(S) and f(10)=3. (a) For small S, write an approximate equation relating R and S near S =... Problem 22E: Let y = f(x) with f(3) = 5 and f(3)=9. (a) For small x, write an approximate equation relating y and... Problem 23E: If t is the number of years since 2014, the population, P, of China,8 in billions, can be... Problem 24E: A city grew in population throughout the 1980s and into the early 1990s. The population was at its... Problem 25E Problem 26E: Analysis of satellite data indicates that the Greenland ice sheet lost approximately 2900 gigatons... Problem 27E: A laboratory study investigating the relationship between diet and weight in adult humans found that... Problem 28E: An economist is interested in how the price of a certain commodity affects its sales. Suppose that... Problem 29E: On May 9, 2007, CBS Evening News had a 4.3 point rating. (Ratings measure the number of viewers.)... Problem 30E: Let W(h) be an invertible function which tells how many gallons of water an oak tree of height h... Problem 31E: The population of Mexico in millions is P = f(t), where t is the number of years since 2014. Explain... Problem 32E: Let f(t) be the number of centimeters of rainfall that has fallen since midnight, where t is the... Problem 33E: Water is flowing into a tank; the depth, in feet, of the water at time t in hours is h(t).... Problem 34E: As the altitude of an object increases, the pressure of the earths atmosphere on the object... Problem 35E: As the distance of an object from the surface of the earth increases, the weight of the object... Problem 36E: The acceleration a, in meters/second2, of a child on a merry-go-round depends on her distance, r... Problem 37E: Let p(h) be the pressure in dynes per cm2 on a diver at a depth of h meters below the surface of the... Problem 38E: Let g(t)be the height, in inches, of Amelia Earhart (one of the first woman airplane pilots) t years... Problem 39E: If g(v) is the fuel efficiency, in miles per gallon, of a car going at v miles per hour, what are... Problem 40E: The function P(d) gives the total electricity, in kWh, that a solar array has generated between the... Problem 41E: Let P be the total petroleum reservoir on Earth in the year t. (In other words, P represents the... Problem 42E: (a) If you jump out of an airplane without a parachute, you fall faster and faster until air... Problem 43E: Let W be the amount of water, in gallons, in a bathtub at time t, in minutes. (a) What are the... Problem 44E: The temperature T of the atmosphere depends on the altitude aabove the surface of Earth. Two... Problem 45E: The Arctic Sea ice extent, the area of sea covered by ice, grows over the winter months, typically... Problem 46E: The depth, h (in mm), of the water runoff down a slope during a steady rain is a function of the... Problem 47E: Average leaf width, w (in mm), in tropical Australia is a function of the average annual rainfall, r... Problem 48E: When an ice dam for a glacial lake breaks, the maximal outflow rate, Q in meters3sec is a function... Problem 49E: The growth rate, R(in cell divisions per hour), of the E. coli bacterium is a function of C(in units... Problem 50E: A companys revenue from car sales, C (in thousands of dollars), is a function of advertising... Problem 51E: In April 2015 in the US, there was one birth every 8 seconds, one death every 12 seconds, and one... Problem 52E Problem 53E: Let P(x) be the number of people of height x inches in the US. What is the meaning of P(66)? What... Problem 54E: When you breathe, a muscle (called the diaphragm) reduces the pressure around your lungs and they... Problem 55E: In Problems 5557, explain what is wrong with the statement. If the position of a car at time t is... Problem 56E: In Problems 5557, explain what is wrong with the statement. A spherical balloon originally contains... Problem 57E: In Problems 5557, explain what is wrong with the statement. A laser printer takes T(P) minutes to... Problem 58E: In Problems 5859, give an example of: A function whose derivative is measured in years/dollar. Problem 59E: In Problems 5859, give an example of: A function whose derivative is measured in miles/day. Problem 60E: Are the statements in Problems 6063 true or false? Give an explanation for your answer. By... Problem 61E: Are the statements in Problems 6063 true or false? Give an explanation for your answer. If y = f(x),... Problem 62E: Are the statements in Problems 6063 true or false? Give an explanation for your answer. If f(t) is... Problem 63E: Are the statements in Problems 6063 true or false? Give an explanation for your answer. If f(t) is... Problem 64E: For Problems 6465, assume g(v) is the fuel efficiency, in miles per gallon, of a car going at a... Problem 65E: For Problems 6465, assume g(v) is the fuel efficiency, in miles per gallon, of a car going at a... format_list_bulleted