The water level in a tank decreases with time according to the following equation: h(t) = 1.8 t² – 96 t + 1280 where h(t) = water level in meters, t = time in seconds (a) Determine the first-order...

I need part (e), and (f), and the solution of the part (a) is on the image.

Extracted text: The water level in a tank decreases with time according to the following equation: h(t) = 1.8 t² – 96 t + 1280 where h(t) = water level in meters, t = time in seconds (a) Determine the first-order differential equation relating= to t. (e) Solve DE in (a) using Laplace Transform. Compare it with the given formula of h(t) (f) Plot h vs t (using the given formula of h(t)), then evaluate the solution in terms of shape, initial level, and final level. You will need the initial condition (h(0)) to solve using laplace and find particular solution. Use b(0) = 1280


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