### Exponential Modeling of Average Annual Wages**Problem Statement:**Watch the video and then solve the problem given below.**Instructions:**1. **Watch Video:** [Click here to watch the video.]2. **Data Analysis:** The accompanying table shows the average annual wage for a country, in thousands of dollars, for selected years from 1980 and projected to 2050. Complete parts a through c.**Tasks:****a. Find an Exponential Function:** Find an exponential function that models these data, with $ x $ equal to the number of years after 1980 and $ y $ equal to the average annual wage in thousands of dollars. The general form of the exponential function is: \[ y = \] (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)**b. Graph the Model:** Graph the model and the data on the same axes. Choose the correct graph below.**Graphs Provided:**- All graphs are displayed in a viewing window of [0, 70] for the x-axis and [0, 250] for the y-axis. - **Option A:** Displays a curve that rises gradually, fitting most data points closely. - **Option B:** Similar to Option A, with a slightly steeper curve fitting the data points. - **Option C:** Shows a more linear curve not closely following the data trend. - **Option D:** Displays a curve with little to no fit to the data, diverging noticeably.**Selection:**Select the graph that best fits the model and the data.**Next Steps:**Proceed to the next part once you’ve identified the correct graph. **Educational Content on the Projection of Average Annual Wages****Introduction:**The following content is designed to help students understand how data is used to predict future economic trends, particularly the average annual wage in a given country.**Video Resource:**Begin by watching the instructional video linked here: [Click here to watch the video].**Data Overview:**The accompanying table displays the historical and projected average annual wage, measured in thousands of dollars, for selected years from 1980 to 2050. **Data Table:**| Year | Average Annual Wage ($ thousands) ||------|----------------------------------|| 1980 | 11.9 || 1990 | 23.7 || 2000 | 34.3 || 2010 | 40.3 || 2012 | 41.9 || 2014 | 46.6 || 2016 | 51.7 || 2018 | 59.8 || 2020 | 63.4 || 2025 | 67.3 || 2030 | 81.8 || 2035 | 112.5 || 2040 | 138.2 || 2045 | 163.3 || 2050 | 181.2 |**Graphical Analysis:**Students are provided with two graphs, labeled A and B, that illustrate the trend of the average annual wage over time. Both graphs utilize a viewing window of `[70, 210]` by `[0, 250]`.**Predictive Modeling Exercise:**- **Question:** What does the model predict that the average annual wage will be in 2040? *Answer Calculation:* According to the model, the average annual wage in 2040 is projected to be **138.2 thousand dollars**. Note that precise rounding may be required as needed.**Conclusion:**This exercise highlights the importance of using historical data and predictive models to understand potential future trends in economics. Students are encouraged to explore these projections critically and consider external factors that might influence actual outcomes.

Given information Year Year Average annual wage (,000) 1980 0 11.9 1990 10 23.7 2000 20 34.3 2010 30 40.3 2012 32 41.9 2014 34 46.6 2016 36 57.1 2018 38 59.8 2020 40 63.4 2025 45 67.3 2030 50 87.8 2035 55 112.5 2040 60 138.2 2045 65 163.3 2050 70 181.2Part a) To find exponential function steps to be followed: 1) To select the data 2) insert the scatter chart 3) click on the data point 4) Add the trend line and select exponential and display the equation By using the above steps Y=13.933e0.0374x Part b) Therefore, the model and data graph looks like the It is similar to option A graph So, option A is the correct option Options B, C, and D are incorrect since the plotted graph is not similar to the graphs given in the options.Part c) The forecasted value is determined by the above model. Year Year Average annual wage (,000) Forecasted value 1980 0 11.9 13.933 1990 10 23.7 19.575 2000 20 34.3 27.502 2010 30 40.3 38.639 2012 32 41.9 41.358 2014 34 46.6 44.268 2016 36 57.1 47.383 2018 38 59.8 50.717 2020 40 63.4 54.286 2025 45 67.3 64.345 2030 50 87.8 76.269 2035 55 112.5 90.401 2040 60 138.2 107.153 2045 65 163.3 127.009 2050 70 181.2 150.545 Formula table: The average annual wage in the year 2040=107.153=107153 from the above table.

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The accompanying table shows the average annual wage for a country, in thousands of dollars, for selected years from 1980 and projected to 2050. Complete parts a throu a. Find an exponential function that models these data, with x equal to the number of years after 1980 and y equal to the average annual wage in thousands of dollars. The equation of an exponential function that models the data is y= (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) b. Graph the model and the data on the same axes. Choose the correct graph below. All graphs are shown in a [0,70,10] by [0,250,50] viewing window. O A. O B. O C. OD.

The accompanying table shows the average annual wage for a country, in thousands of dollars, for selected years from 1980 and projected to 2050. Complete parts a throu a. Find an exponential function that models these data, with x equal to the number of years after 1980 and y equal to the average annual wage in thousands of dollars. The equation of an exponential function that models the data is y= (Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) b. Graph the model and the data on the same axes. Choose the correct graph below. All graphs are shown in a [0,70,10] by [0,250,50] viewing window. O A. O B. O C. OD.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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