The table displays data on corn yield (in bushels per acre) and total production (in millions of bushels) in a country for selected years since 1950. Here, $ x $ denotes the number of years since 1900. The goal is to determine a logarithmic regression model ($ y = a + b \ln x $) for predicting yield and to estimate the yield for the year 2023.### Table Data:- **Year 1950**: $ x = 50 $, Yield = 41- **Year 1960**: $ x = 60 $, Yield = 57- **Year 1970**: $ x = 70 $, Yield = 83- **Year 1980**: $ x = 80 $, Yield = 93- **Year 1990**: $ x = 90 $, Yield = 116- **Year 2000**: $ x = 100 $, Yield = 142- **Year 2010**: $ x = 110 $, Yield = 154### Instructions for Calculations:1. **Complete the Regression Model**: $ y = \left[ \, \right] + \left[ \, \right] \ln x $. Round to one decimal place as needed.2. **Estimate Yield for 2023**: Provide the estimated yield in bushels per acre, rounded to the nearest integer. This activity involves fitting a logarithmic regression equation to the given data, which is a common method used in predicting trends and is especially useful when growth rates are expected to change at a diminishing rate.

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Answered: The table shows the yield (in bushels…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The table shows the yield (in bushels per acre) and the total production (in millions of bushels) for corn in a country for selected years since 1950. Let x represent years since 1900. Find a logarithmic regression model (y = a +b ln x) for the yield. Estimate the yield in 2023. Year 1950 1960 Yield 50 37 60 1970 1980 60 84 93 70 80 1990 90 116 2000 2010 100 136 110 157 The regression model is y =+( In x. (Round to one decimal place as needed.) bushels/acre. The estimated yield in 2023 is (Round to the nearest integer.)
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