Answer
The force of the water against the dam increases as the depth of the water increases.
Work Step by Step
We are given the function:
$F(y)=149.76\sqrt{10}y^{5/2}$
Compute $F(y)$ for $y=5,10,20,30,40$:
$F(5)=149.76\sqrt{10}(5^{5/2})\approx 26,474.08$
$F(10)=149.76\sqrt{10}(10^{5/2})=149,760.00$
$F(20)=149.76\sqrt{10}(20^{5/2})\approx 847,170.49$
$F(30)=149.76\sqrt{10}(30^{5/2})\approx 2,334,527.36$
$F(40)=149.76\sqrt{10}(40^{5/2})=4,792,320.00$
Place the results in the table.
We notice that as the depth of the water increases, the force of the water against the dam increases.
