Answered: The table lists future concentrations… | bartleby

Advanced Engineering Mathematics

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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Question

The table presents projected future concentrations of a specific greenhouse gas in parts per billion (ppb), assuming current trends persist.

### Table of Gas Concentrations

| Year | 2010 | 2015 | 2020 | 2025 | 2030 |
|------|------|------|------|------|------|
| Gas (ppb) | 0.66 | 0.77 | 0.89 | 1.03 | 1.19 |

### Questions

#### a. Find Constants for the Growth Model
- Define \( x = 0 \) for the year 2010 and \( x = 20 \) for the year 2030.
- Determine constants \( C \) and \( a \) so that the equation \( f(x) = Ca^x \) accurately represents the data in the table.

\[
C = \_ \_
\]
\[
a \approx \_ \_ \_ \_ \_ \_
\]
(Round to the nearest hundredth.)

#### b. Estimate for 2023
- Calculate the estimated gas concentration for the year 2023.

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