The depth of water in a harbour varies as a function of time. The maximum depth is 9 feet and the minimum depth is 1 foot. The depth can be modelled with a sinusoidal function that has a period of 12 hours. If the depth is 5 feet at 12 midnight, and is increasing, 1. Create an algebraic model to predict the depth of the water as a function of time. Justify your reasoning. 2. The water must be at least 7 feet for Annie’s fishing boat to safely navigate the harbour. She wants to enter the harbour during the afternoon. a. Create a graph of this function using technology. b. What is the earliest time she can enter the harbour? c. How long can she safely stay in the harbour?
The depth of water in a harbour varies as a function of time. The maximum depth is 9 feet and the minimum depth is 1 foot. The depth can be modelled with a sinusoidal function that has a period of 12 hours. If the depth is 5 feet at 12 midnight, and is increasing, 1. Create an algebraic model to predict the depth of the water as a function of time. Justify your reasoning. 2. The water must be at least 7 feet for Annie’s fishing boat to safely navigate the harbour. She wants to enter the harbour during the afternoon. a. Create a graph of this function using technology. b. What is the earliest time she can enter the harbour? c. How long can she safely stay in the harbour?
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 depth of water in a harbour varies as a function of time. The maximum depth is
9 feet and the minimum depth is 1 foot. The depth can be modelled with a sinusoidal
function that has a period of 12 hours. If the depth is 5 feet at 12 midnight, and is
increasing,
1. Create an algebraic model to predict the depth of the water as a function of time.
Justify your reasoning.
2. The water must be at least 7 feet for Annie’s fishing boat to safely navigate the
harbour. She wants to enter the harbour during the afternoon.
a. Create a graph of this function using technology.
b. What is the earliest time she can enter the harbour?
c. How long can she safely stay in the harbour?
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