World production of copper, in millions of tons per year, from 1900 to 2000 is given by C = 0.5 × 1.033°, where t is the time in years since 1900. t (a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places.) X million tons (b) If this model were extended to 2026, how could you use your knowledge of copper production in 2025 to estimate copper production in 2026? To estimate copper production in 2026 we would multiply copper production in 2025 by

World production of copper, in millions of tons per year, from 1900 to 2000 is given by C = 0.5 × 1.033°, where t is the time in years since 1900. t (a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places.) X million tons (b) If this model were extended to 2026, how could you use your knowledge of copper production in 2025 to estimate copper production in 2026? To estimate copper production in 2026 we would multiply copper production in 2025 by

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### World Copper Production Model

#### Model Description:

The world production of copper, measured in millions of tons per year, from 1900 to 2000, is modeled by the equation:

\[ C = 0.5 \times 1.033^t \]

where $ t $ represents the time in years since 1900.

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#### Questions:

**(a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places.)**

\[ \_\_\_\_\_\_\_ \text{million tons} \]

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**(b) If this model were extended to 2026, how could you use your knowledge of copper production in 2025 to estimate copper production in 2026?**

To estimate copper production in 2026 we would multiply copper production in 2025 by

\[ \_\_\_\_\_\_\_ \]

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#### Explanation of the Formulas:

**For part (a):**
- To determine the production level for the year 2000, you will need to calculate $ t $ as follows: $ t = 2000 - 1900 $.
- Substitute $ t = 100 $ in the given model and solve for $ C $.

**For part (b):**
- To extend the model to 2026, understand the annual growth factor from the model.
- Identify how you can use the growth rate $ 1.033 $ to project the next year's production from the current year.

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