The depth of water, 𝑑, in meters, varies with the tides throughout the day and can be modeled by the equation 𝐷(𝑡) = 2.5 cos[0.675(𝑡 − 3.5)] + 4.3, where 𝑡 is the number of hours past 12 AM.
(A)- Jaya claims that the depth is overall increasing from 8 AM to 11 AM by 0.15 m per hour. Is Jaya’s claim, correct? Describe and explain the steps you would take to check Jaya’s claim. Use terminology and formulae learned in this unit. Provide calculations as
needed
(B)- Abithan claims that at exactly 10 AM, the depth is decreasing by 0.5 m per hour. Is Abithan’s claim, correct? Describe and explain the steps you would take to check Abithan’s claim. Use terminology and formulae Provide calculationsas needed.
B has been answered twice already. See a few previous posts.
As for A, just find D'(t) and see whether it is positive or negative. The assertion as given is clearly false, since the rate of change is not constant. If you mean to say that the average rate of change over that interval is 0.15 m/s, then calculate
(D(11)-D(8))/(11-8) and check