Concept explainers
Modeling Data A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. The results for the first 2 minutes are recorded in the table.
t |
0 |
15 |
30 |
45 |
60 |
T |
25.2 |
36.9 |
45.5 |
51.4 |
56.0 |
t |
75 |
90 |
105 |
120 |
|
T |
59.6 |
62.0 |
64.0 |
65.2 |
(a) Use the regression capabilities of a graphing utility to find a model of the form
(b) Use a graphing utility to graph
(c) A rational model for the data is
Use a graphing utility to graph
(d) Find
(e) Interpret the result in part (d) in die context of the problem. Is it possible to do this type of analysis using
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Calculus (MindTap Course List)
- Graphing Discrete Data Plot the data from the table in Exercise S-2. S-2. Testing Data for Linearity Test the following data to see whether they are linear. x 2 4 6 8 y 12 17 21 25arrow_forwardDraw a best-fit line for the plotted data.arrow_forwardMaking a Linear Model Make a linear model for the data in Exercise S-1. S-1. Testing Data for Linearity Test the following data to see whether they are linear. x 2 4 6 8 y 12 17 22 27arrow_forward
- Draw a scatter plot for the data in Table 2. Then determine whether the data appears to belinearly related.arrow_forwardNoise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.arrow_forwardBiology The metabolic rate of an ectothermic organism increases with increasing temperature within a certain range. Experimental data for the oxygen consumption C (in microliters per gram per hour) of a beetle at certain temperatures can be approximated by the model C=0.45x21.65x+50.75,10x25 where x is the air temperature in degrees Celsius. a The oxygen consumption is 150 microliters per gram per hour. What is the air temperature ? b When the air temperature increases from 10C to 20C, the oxygen consumption increases by approximately what factor ?arrow_forward
- Further Verification of Newtons Second LawThis exercise represents a hypothetical implementation of the experiment suggested in the solution of part 6 of Example 3.7. A mass of 15 kilograms was subjected to varying accelerations, and the resulting force was measured. In the following table, acceleration is in meters per second per second, and force is in newton. Acceleration Force 8 120 11 165 14 210 17 255 20 300 a. Construct a table of differences and explain how it shows that these data are linear. b. Find a linear model for the data. c. Explain in practical terms what the slope of this linear model is. d. Express, using functional notation, the force resulting from an acceleration of 15 meters per second per second, and then calculate that value. e. Explain how this experiment provides further evidence for Newtons second law of motion.arrow_forwardDoes the following table represent a linear function ? If so, find the linear equation that models the data.arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning