Question

The depth of water, 𝑑, in metres, varies with the tides throughout the day and can be modelled by the equation 𝐷(𝑑) = 2.5π‘π‘œπ‘ (0.675(𝑑 βˆ’ 3.5)) + 4.3, where 𝑑 is the number of hours past 12π‘Žπ‘š.

Abithan claims that at exactly 10π‘Žπ‘š, the depth is decreasing by 0.5π‘š per hour. Is Abithan’s claim, correct? Describe and explain the steps you would take to check Abithan’s claim. Use terminology and formulae learned in this unit. Provide calculations as needed.

Answers

oobleck
2.5cos(0.675(t βˆ’ 3.5)) + 4.3
D' = -1.6875sin(0.675(t βˆ’ 3.5))
10am is 10 hours past midnight, so just find D'(10)

please do not blindly regurgitate specific instructions on how to proceed. I am not responsible for following your teacher's directions, and I certainly have no idea about the "terminology and formulae learned in this unit."
Anonymous
t = 10 hours past midnight
dD/dt = -2.5 (0.675) sin (0.675(𝑑 βˆ’ 3.5))

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