Energy use Energy use per dollar of GDP indexed to 1980 means that energy use for any year is viewed as a percent of the use per dollar of GDP in 1980. The following data show the energy use per dollar of GDP, as a percent, for selected years from 1985 and projected to 2035.
Energy Use per Dollar of GDP
Year | Percent | Year | Percent |
1985 | 83 | 2015 | 51 |
1990 | 79 | 2020 | 45 |
1995 | 75 | 2025 | 41 |
2000 | 67 | 2030 | 37 |
2005 | 60 | 2035 | 34 |
2010 | 56 |
Source: U.S. Department of Energy
These data can be modeled with the function
(a) Find E'(t).
(b) Use this model to find and interpret the instantaneous rates of change of energy use per dollar of GDP in 2000 and 2025.
(c) Use the data in the table to find an average rate of change that approximates the 2025 instantaneous rate.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
MATHEMATICAL APPL...(LL)-PKG.>CUSTOM<
- Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forwardTable 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?arrow_forwardFind the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forward
- (e) Test the hypothesis Ho : B1 = 10 versus H1 :ß, # 10 using a = 0.01. Ho and conclude the slope v 10 at a = 0.01. (d) Test the hypothesis Ho : Bo = 0 versus H1 : Bo + 0 using a = 0.01. Ho and conclude that the intercept be included in the model.arrow_forwardThe financial aid office at Burke University produced an internal report on the number of students receiving scholarships. Students receiving scholarships Year Students 2017 18 2018 35 2019 28 2020 30 2021 18 According to the table, what was the rate of change between 2017 and 2018? students per yeararrow_forwardthe table shows the percent of households with internet access for selected years from 2009 and projected through 2015. Year Percent of households 2009 67 2010 70 2011 72.5 2012 75 2013 76.5 2014 77.2 2015 78 Use the model to predict the percent of households with internet access in 2022.arrow_forward
- Which of the following mortality rates use the estimated total mid-year population as its denominator? [ O Sex-specific mortality rate O Crude mortality rate O Age-specific mortality rate Cause-specific proportionate mortality rate A new treatment is developed that prevents death but does not produce recovery from disease. Which of the following will occur? O Prevalence will decrease O Incidence will decrease O Incidence will increase Prevalence will increasearrow_forwardThe following table gives information on the Consumer Price Index (Base = 1982–84) and the monthly take-home pay of Bill Martin, an employee at Ford Motor Corporation, from 1982−84 and 2018. Consumer Price Index Mr. Martin’s Monthly Year (1982−84 = 100) Take-Home Pay 1982−84 100.0 $ 600 2018 251.107 7,000arrow_forwardThe owner of Showtime Movie Theaters, Inc., would lke to predict weekly gross revenue as a function of advertising expenditures Historical data for a sample of eight wecks follow Weekly Gross Revenue ($1,000s) Television Advertising ($1,000s) Newspaper Advertising ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x), in thousands of dolars, and newspaper advertising (x,), in thousands of dollars. The estimated regression equation was = 83.2 + 2.29x, + 1.30x. (a) What is the gross revenue (in dollars) expected for a week when $5,000 is spent on television advertising (x5) and $1,500 is spent on newspaper advertising (, 1.5)? (Round your answer to the nearest dollar.) $06600 (b) Provide a 95% confidence interval (in dolars) for the mean revenue of all weeks with the expenditures listed in part (a).…arrow_forward
- MORTALITY RATE Table 3.5 provides the number of deaths from all causes and from accidents (unintentional injuries) by age group in the United States in 2002. Review the following rates. Determine what to call each one, then calculate it using the data provided in Table. 1. Unintentional-injury-specific mortality rate for the entire population. Calculate cause-specific mortality rate. 2. All-cause mortality rate for 25-34 years old. Calculate the age-specific mortality rate. 3. All-cause mortality among males. Calculate the sex-specific mortality rate. 4. Unintentional-injury specific mortality among 25 to 34 years old males. Calculate the is a cause-specific, age-specific, and sex-specific mortality rate Table 3.5 All-Cause and Unintentional Injury Mortality and Estimated Population by Age Group, For Both Sexes and For Males Alone- United States, 2002 All Races, Both Sexes All Races, Males Age group (years) All Causes Unintentional Estimated All Unintentional Estimated Injuries Pop. (x…arrow_forwardB4. A company has collected and smoothened its historical yearly sales data of a product from 2015 up to 2021. The following table shows the sales and moving average figures. Sales Three-year moving avcrage Year Five-ycar moving avcrage (S thousands) 2015 2016 326.0 324.0 E 367.4 2017 344.0 2018 383.0 371.0 2019 B. 389.0 2020 398.0 D 2021 428.0 Calculate the missing values of4, B, C, D. E and F(Correct to I decimal place). B5. A lottery consists of 49 balls numbered 1 through 49 and 6 of them are drawn at random. (a) You can pick 6 different numbers for a betting ticket. How many selections are possible? (b) If prizes will be paid to those picking 4 to 6 drawn numbers, how many winning selections are possible? రarrow_forwardThe number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table: Month Temp. Usage/1000 Month Temp. Usage/1000 Jan. 21 185.79 July. 68 621.55 Feb. 24 214.47 Aug. 74 675.06 Mar. 32 288.03 Sept. 62 562.03 Apr. 47 424.84 Oct. 50 452.93 May 50 454.58 Nov. 41 369.95 June 59 539.03 Dec. 30 273.93 Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual. Test for significance of regression using α=0.01 (Use ANOVA). Calculate the r2 of the model. Find a 99% CI for .arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,