Concept explainers
Health The temperature T (in degrees Fahrenheit) of a person during an illness can be modeled by the equation
(a) Use a graphing utility to graph the function. Be sure to choose an appropriate window.
(b) Do the slopes of the tangent lines appear to be positive or negative? What does this tell you?
(c) Evaluate the function for
(d) Find dT/dt and explain its meaning in this situation.
(e) Evaluate dT/dt for
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus: An Applied Approach (MindTap Course List)
- Use the Vertical Line Test to determine whether the graph represents y as a function of x.arrow_forwardThe half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forwardCeramics When the temperature of a pot in a kiln is 1200, an artist turns off the heat and leaves the pot to cool at a controlled rate of 18 per hour. Express the temperature of the pot in degrees Celsius as a function of the time t in hours since the kiln was turned off.arrow_forward
- Target heart rate The target heart rate f(x), in beats per minute, at which a person should train to get an effective workout is a function of the persons age x in years. If f(x)=0.6x+132, find the target heart rate for a 45-year-old college professor.arrow_forwardSlope If a building is 100 feet tall and is viewed from a spot on the ground 70 feet away from the base of the building, what is the slope of a line from the spot on the ground to the top of the building?arrow_forwardFor a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is modeled by v=0.85sint/3, where t is the time (in seconds). a Find the time for one full respiratory cycle. b Find the number of cycles per minute. c Sketch the graph of the velocity function. Use the graph to confirm your answer in part a by finding two times when new breaths begin. (Inhalation occurs when v0, and exhalation occurs when v0.)arrow_forward
- Why does the horizontal line test tell us whether the graph of a function is one-to-one?arrow_forwardA car’s value varies inversely with its age. Elena bought a two-year-old car for $20,000. a. Write the equation of variation. b. What will be the value of Elena’s car when it is 5 years old?arrow_forwardUse your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning