The depth of water, 𝑑, in metres, varies with the tides throughout the day and can be modelled by the equation 𝐷(𝑡) = 2.5𝑐𝑜𝑠(0.675(𝑡 − 3.5)) + 4.3, where 𝑡 is the number of hours past 12𝑎𝑚.

Question

Abithan claims that at exactly 10𝑎𝑚, the depth is decreasing by 0.5𝑚 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.

Answer 1

2.5cos(0.675(t − 3.5)) + 4.3
D' = -1.6875sin(0.675(t − 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."

Answer 2

t = 10 hours past midnight
dD/dt = -2.5 (0.675) sin (0.675(𝑡 − 3.5))