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,
Create an algebraic model to predict the depth of the water as a function of time. Justify your reasoning.
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.
i. Create a graph of this function using technology.
What is the earliest time she can enter the harbour?
How long can she safely stay in the harbour?
Answers
Given : 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
depth is 5 feet at 12 midnight,
The water must be at least 7 feet for Annie’s fishing boat to safely navigate the harbour.
To Find : graph of this function using technology.
earliest time she can enter the harbour?
How long can she safely stay in the harbour?
Solution:
Lets represent 12 midnight as 0
maximum depth is 9 feet and the minimum depth is 1 foot
(9 + 1)/2 = 5
9 - 1 = 8 = 4(2)
Period 12 hr Hence 2πx/12 = πx/6
x represent time
f(x) represent Depth
at mid night Depth is increasing Hence function is
f(x)=5 + 4 sin((π x)/(6))
Between 13 hrs and 17 hrs depth is above 7 ft
Hence from 1 PM to 5 PM
earliest time she can enter the harbour is 1 PM
She can stay for 17 - 13 = 4 hrs
Learn More:
Number of real solution of the equation [tex]sqrt{log_{10}(-x)} = log ...
brainly.in/question/9443251
the no of real solutions of the equation sinx=x^2+3x+4 is - Brainly.in
brainly.in/question/10656718
Answer:a. y=4sin(pi t/6) +5
Step-by-step explanation: