The image contains an educational exercise related to modeling average annual wages over time using an exponential function. It includes a table, some text questions, and two small graphs.### Table: Average Annual WageThe table presents data on average annual wages in thousands of dollars for various years:- 1970: $9.6- 1980: $24.8- 1990: $26.3- 2000: $45.2- 2005: $52.8- 2006: $53.7- 2010: $57.3- 2015: $72.9- 2020: $95.6- 2025: $115.6- 2030: $126.6- 2035: $156.7- 2040: $195.7### Questions and Answers:1. **Find an Exponential Function:** Students are prompted to find an exponential function to model the data, using x as the number of years after 1970.2. **Graph the Model:** The task involves graphing both the model and data on the same axes. Two graphs are shown, though details are not vivid.3. **Predicting Wage in 2030:** - According to the model, the average annual wage in 2030 is predicted to be $126.6 thousand. - This is an interpolation because 2030 falls within the range of the given years.4. **Predict $230,000 Wage:** - The model predicts that the average annual wage will reach $230,000 in a certain year, which the student must calculate by rounding to the nearest year.### Graphs:The graphs depict data points and a model line, illustrating the trend over the years. Due to image clarity, specific details are limited, but they represent wage growth over time aligned with the data table.This exercise is designed to help students understand how to apply mathematical modeling to real-world data and interpret the results within a given context. The accompanying table shows the average annual wage for a country, in thousands of dollars, for selected years from 1970 and projected to 2040.a. Find an exponential function that models these data, with *x* equal to the number of years after 1970 and *y* equal to the average annual wage in thousands of dollars.b. Graph the model and the data on the same axes.c. What does the model predict that the average annual wage will be in 2030? Is this interpolation or extrapolation?d. When does the model predict that the average annual wage will reach $230,000?---a. 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 on the same axis as the data. Choose the correct graph below. All graphs are shown in a [0,70,110] by [0,250,50] viewing window.Options:- Graph A- Graph B- Graph C- Graph Dc. According to the model, the average annual wage in 2030 will be $_____ thousand. (Round to one decimal place as needed.)---**Graph Explanation:**The graph options (A, B, C, D) are different visual representations of the data with a model plotted. Each graph displays data points and an exponential curve, indicating potential models for the data set. The correct graph must accurately fit the given data points.

Given information Year Average annual wage (,000) 1970 9.6 1980 24.8 1990 26.3 2000 45.6 2002 48.2 2004 53.7 2006 57.8 2008 56.3 2010 72.9 2015 72.3 2020 86.5 2025 115.6 2030 136.6 2035 156.7 2040 195.7Part 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 Exponential equation Y=12.989e0.0394X The forecasted value is determined by the above model Average Annual wage=12.989e^0.0394*X Part b) Predicted value Year Year Average annual wage (,000) Forecasted values 1970 0 9.6 12.989 1980 10 24.8 19.26139523 1990 20 26.3 28.56273355 2000 30 45.6 42.35569325 2002 32 48.2 45.82834772 2004 34 53.7 49.58571784 2006 36 57.8 53.65114685 2008 38 56.3 58.04989187 2010 40 72.9 62.80928076 2015 45 72.3 76.48562735 2020 50 86.5 93.13991691 2025 55 115.6 113.4205788 2030 60 136.6 138.1172339 2035 65 156.7 168.1914385 2040 70 195.7 204.8141219 Formula table: Part c) Average annual wages as per the model in 2030=136.6 =136600 Salary of 2030 s interpolation since it comes within the range. Interpolation is a method of predicting the data within the given range. Part d) To find the forecasted value for the wages 230000, the goal-seek function should be used. Step 1) Go to the Data ribbon Step2) drop down the what-if analysis Step 3) Select the goal-seek function By clicking Ok we get the result In 2043, average annual wage=229.999=230000

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The accompanying table shows the average annual wage for a country, in thousands of dollars, fo . Find an exponential function that models these data, with x equal to the number of years after 1 b. Graph the model and the data on the same axes. c. What does the model predict that the average annual wage will be in 2030? Is this interpolation d. When does the model predict that the average annual wage will reach $230,000? Click on the icon to view the data table

The accompanying table shows the average annual wage for a country, in thousands of dollars, fo . Find an exponential function that models these data, with x equal to the number of years after 1 b. Graph the model and the data on the same axes. c. What does the model predict that the average annual wage will be in 2030? Is this interpolation d. When does the model predict that the average annual wage will reach $230,000? Click on the icon to view the data table

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

The image contains an educational exercise related to modeling average annual wages over time using an exponential function. It includes a table, some text questions, and two small graphs.

### Table: Average Annual Wage
The table presents data on average annual wages in thousands of dollars for various years:

- 1970: $9.6
- 1980: $24.8
- 1990: $26.3
- 2000: $45.2
- 2005: $52.8
- 2006: $53.7
- 2010: $57.3
- 2015: $72.9
- 2020: $95.6
- 2025: $115.6
- 2030: $126.6
- 2035: $156.7
- 2040: $195.7

### Questions and Answers:
1. **Find an Exponential Function:**
Students are prompted to find an exponential function to model the data, using x as the number of years after 1970.

2. **Graph the Model:**
The task involves graphing both the model and data on the same axes. Two graphs are shown, though details are not vivid.

3. **Predicting Wage in 2030:**
- According to the model, the average annual wage in 2030 is predicted to be $126.6 thousand.
- This is an interpolation because 2030 falls within the range of the given years.

4. **Predict $230,000 Wage:**
- The model predicts that the average annual wage will reach $230,000 in a certain year, which the student must calculate by rounding to the nearest year.

### Graphs:
The graphs depict data points and a model line, illustrating the trend over the years. Due to image clarity, specific details are limited, but they represent wage growth over time aligned with the data table.

This exercise is designed to help students understand how to apply mathematical modeling to real-world data and interpret the results within a given context.

The accompanying table shows the average annual wage for a country, in thousands of dollars, for selected years from 1970 and projected to 2040.

a. Find an exponential function that models these data, with *x* equal to the number of years after 1970 and *y* equal to the average annual wage in thousands of dollars.

b. Graph the model and the data on the same axes.

c. What does the model predict that the average annual wage will be in 2030? Is this interpolation or extrapolation?

d. When does the model predict that the average annual wage will reach $230,000?

---

a. 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 on the same axis as the data. Choose the correct graph below. All graphs are shown in a [0,70,110] by [0,250,50] viewing window.

Options:
- Graph A
- Graph B
- Graph C
- Graph D

c. According to the model, the average annual wage in 2030 will be $_____ thousand. (Round to one decimal place as needed.)

---

**Graph Explanation:**
The graph options (A, B, C, D) are different visual representations of the data with a model plotted. Each graph displays data points and an exponential curve, indicating potential models for the data set. The correct graph must accurately fit the given data points.

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