The force Fin tons of water against the face of a dam is est

The force F(in tons) of water against the face of a dam is estimated by the function F(y)=215.28squareroot 10 y^5/2 where y is the depth of the water (in feet). Compute the table (Round your answers to nearest integer.) Use the table approximate the depth at which the force against the dam is 1,000,000 tons. Verify your answer graphically How could find better estimate? BY completing the table for values of y between 0 and 5 BY completing the table for values of y between 5 and 10 BY completing the table for values of y between 10 and 20 BY completing the table for values of y between 20 and 30 BY completing the table for values of y between 30 and 40

Solution

We are given F (y) = 215.28 ( 10)y^5/2 = 215.28*10^1/2y^5/2    = 680.775y^2.5 ( as 10^1/2 = 3.16228 approx and 215.28* 10^1/2 = 680.775) .  The required table has been completed as under:

From the above table, it is apparent that the force against the dam is 100000 tons at a depth of about 5ft ( actually between 5 and 10 ft; the force at 5 ft depth is closer to 100000 than that at 10 ft depth)

A better estimate can be found by completing the table for values of y between 5 and 10 ( as 100000 is between 38056 and 215280)

y	5	10	20	30	40
F(y)	38056	215280	1217807	33558822	6888959