Determine w2

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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Determine w2

**Transcription for Educational Website**

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**SHORT ANSWER: Complete the statement or answer the question.**

**Problem:**

Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to evaporation every week. Approximately 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoir at the end of each week is given by the recursively defined sequence:

- \( w_0 = 300 \)
- \( w_n = (0.9993)w_{n-1} + 0.15 \)

Determine the amount of water in the reservoir at the beginning of the second week. That is, determine \( w_2 \).

Write your answer in the space provided or on a separate sheet of paper.

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This section presents a problem involving the Lexington Reservoir, where you are required to use a recursive formula to calculate the water level at a specific time. The problem accounts for both water loss through evaporation and water added weekly.
Transcribed Image Text:**Transcription for Educational Website** --- **SHORT ANSWER: Complete the statement or answer the question.** **Problem:** Lexington Reservoir has 300 million gallons of water. About 0.07% of the water is lost to evaporation every week. Approximately 150,000 gallons of water enter the reservoir every week. The amount of water in the reservoir at the end of each week is given by the recursively defined sequence: - \( w_0 = 300 \) - \( w_n = (0.9993)w_{n-1} + 0.15 \) Determine the amount of water in the reservoir at the beginning of the second week. That is, determine \( w_2 \). Write your answer in the space provided or on a separate sheet of paper. --- This section presents a problem involving the Lexington Reservoir, where you are required to use a recursive formula to calculate the water level at a specific time. The problem accounts for both water loss through evaporation and water added weekly.
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