**Table 3: US Corn Production**This table displays data on corn yield and total production in the United States for selected years since 1950.| Year | Yield (bushels per acre) | Total Production (million bushels) ||------|--------------------------|-------------------------------------|| 1950 | 37.6 | 2,782 || 1960 | 55.6 | 3,479 || 1970 | 81.4 | 4,802 || 1980 | 97.7 | 6,867 || 1990 | 115.6 | 7,802 || 2000 | 139.6 | 10,192 |**Tasks:**A. Let $ x $ represent years since 1900 and find the logarithmic model for the yield.\[ Y(x) = \_\_\_\_ \]B. What is the $ r^2 $ value for the equation in part A?\[ r^2 = \_\_\_\_ \]C. Let $ x $ represent years since 1900 and find the logarithmic model for the production.\[ P(x) = \_\_\_\_ \]D. What is the $ r^2 $ value for the equation in part C?\[ r^2 = \_\_\_\_ \]

A. Given that, x represents years since 1900. That is x=0 for 1900. Rewrite the Year and Yield as…

(Agriculture). Table 3 shows the yield (in bushels per acre) and the total production (in millions of bushels) for corn in the United States for selected years since 1950. (Use 4 decimal places in all answers.) Table 3: US Corn Production Year Yield (bushels per acre) Total Production (million bushels) 1950 1960 1970 1980 1990 2000 37.6 2,782 55.6 3,479 81.4 4,802 97.7 6,867 115.6 7,802 139.6 10,192 A. Let x represent years since 1900 and find the logarithmic model for the yield. Y(x) = B. What is the r2 value for the equation in part A? C. Let x represent years since 1900 and find the logarithmic model for the production. P(x) = D. What is the r2 value for the equation in part C?

(Agriculture). Table 3 shows the yield (in bushels per acre) and the total production (in millions of bushels) for corn in the United States for selected years since 1950. (Use 4 decimal places in all answers.) Table 3: US Corn Production Year Yield (bushels per acre) Total Production (million bushels) 1950 1960 1970 1980 1990 2000 37.6 2,782 55.6 3,479 81.4 4,802 97.7 6,867 115.6 7,802 139.6 10,192 A. Let x represent years since 1900 and find the logarithmic model for the yield. Y(x) = B. What is the r2 value for the equation in part A? C. Let x represent years since 1900 and find the logarithmic model for the production. P(x) = D. What is the r2 value for the equation in part C?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Table 3: US Corn Production**

This table displays data on corn yield and total production in the United States for selected years since 1950.

| Year | Yield (bushels per acre) | Total Production (million bushels) |
|------|--------------------------|-------------------------------------|
| 1950 | 37.6 | 2,782 |
| 1960 | 55.6 | 3,479 |
| 1970 | 81.4 | 4,802 |
| 1980 | 97.7 | 6,867 |
| 1990 | 115.6 | 7,802 |
| 2000 | 139.6 | 10,192 |

**Tasks:**

A. Let $ x $ represent years since 1900 and find the logarithmic model for the yield.
\[ Y(x) = \_\_\_\_ \]

B. What is the $ r^2 $ value for the equation in part A?
\[ r^2 = \_\_\_\_ \]

C. Let $ x $ represent years since 1900 and find the logarithmic model for the production.
\[ P(x) = \_\_\_\_ \]

D. What is the $ r^2 $ value for the equation in part C?
\[ r^2 = \_\_\_\_ \]

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