The depth of a river at a certain point is modeled by the function W defined above, where W(t) is measured in feet and time T is measured in hours

(a) The meaning of W'(8) is the rate of change of the depth of the water at time t = 8 hours is -0.8 ft/hr

(b) The tangent line equation is Y = 0.79×t +6.143

Therefore, W(3.5) ≤ 9 as 0.79×3.5 +6.143 = 8.908 < 9

(c) is

Step-by-step explanation:

Here we have

(a) To find W'(8) we have

W(8) =

Therefore, W'(8) given by the following relation;

∴

The meaning of W'(8) is the rate of change of the depth of the water at time t = 8 hours = -0.8 ft/hr

b) Here we have the line tangent is given by the slope of the graph at the point t = 3, therefore we have

W'(t), t = 3 =

The tangent line equation is Y = 0.79×t +6.143

Therefore, W(3.5) ≤ 9 as 0.79×3.5 +6.143 = 8.908 < 9

c) where W(t) =

 = .