Concept explainers
How do You See it? An electronically controlled thermostat in a home is programmed to lower the temperature automatically during the night. The temperature in the house T (in degrees Fahrenheit) is given in terms of t, the time in hours on a 24-hour clock (see figure).
(a) Explain why T is a function of t.
(b) Approximate T(4) and T(15).
(c) The thermostat is reprogrammed to produce a temperature H for which
How does this change the temperature?
(d) The thermostat is reprogrammed to produce a temperature H for which
How does this change the temperature?
Trending nowThis is a popular solution!
Chapter 1 Solutions
Calculus: An Applied Approach (MindTap Course List)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Mathematics for Calculus - 6th Edition
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
- Tax Owed The income tax T owed in a certain state is a function of the taxable income I, both measured in dollars. The formula is T=0.11I500 a. Express using functional notation the tax owed on a taxable income of 13, 000, and then calculate that value. b. If your taxable income increases from 13,000 to 14,000, by how much does your tax increase? c. If your taxable income increases from 14,000 to 15,000, by how much does your tax increase?arrow_forwardThe function P(h)=14.7(0.5)^h/3.6 models, the atomspheric pressure, P, (in pounds per square inch) as a function of the height, h,(in miles above sea level). Determine the atmospheric pressure outside in aircraft flying at 58,080 feet (11 miles above sea level).arrow_forwardThe national defense budget expenses V (in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model *Picture of model included* where t represents the year, with t = 0 corresponding to 1990. Use the model to find total veteran expenses in 1999.arrow_forward
- In 1995, the rate of violent crimes in New York City continued to decrease, but at a slower rate than in previous years. Letting ƒ(t) be the rate of violent crime as a function of time, what does this tell you about ƒ(t), ƒ′(t), and ƒ″(t)? Source: The New York Times.arrow_forwardA 500 gallon oil spill undergoes a cleanup process. The company hired to clean the spill can remove 15% of the reaining oil each week. Find a formula to express the total oil left, C, as a function of time t in weeks since the oil spill occurred.arrow_forwardA 5000-gal aquarium is maintained with a pumping system that passes 100 gal of water per minute through the tank. To treat a certain fish malady, a soluble an- tibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te^−(t/50) mg/gal, where t is measured in minutes. The well-stirred mixture flows out of the aquarium at the same rate. (a) Solve for the amount of medicine in the tank as a function of time. (b) What is the maximum concentration of medicine achieved by this dosing and when does it occur? (c) For the antibiotic to be effective, its concentration must exceed 100 mg/gal for a minimum of 60 min. Was the dosing effective? please show all steparrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning