Question

I need help in calculus word problem

Answer 1

A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval 0 <= t <= 18 hours, water is pumped into the tank at the rate \[\large w(t)=95\sqrt{5}\sin^2(\frac{ t }{ 6 })~~~gallons~per~hour.\]During the same time interval, water is removed from the tank at the rate\[\large R(t)=275\sin^2(\frac{ t }{ 3 })~~~gallons~per~hour.\]
(a) Is the amount of water in the tank increasing at time t = 15? Why or why not?

Answer 2

w(t) is the increasing rate
R(t) is the decreasing rate

if w(15) > R(15) then the amount of water is increasing
if w(15) < R(15) then the amount of water is decreasing

Answer 3

1. Plug in 15 for t in w(t) and R(t) to find the rates at time 15.
2. See if it's being pumped in ( w(t) ) faster than its being drained ( r(t) )
3. Decide

Answer 4

Thank you, I will try doing that.

Answer 5

Ok, now how do I figure out the gallons of water in the tank at t = 18?
@sooobored @issimplcalcus

Answer 6

integration from 0->18

then add the constant of 1200 gal

Answer 7

Ok, thank you!

Answer 8

since integration of w(t) will give you the total amount of water added for the duration
and integration of H(t) will give you the total amount of water removed for the duration

sum that up with the initial volume of water, and you should get the total at t=18

Answer 9

Wait, shouldn't you subtract instead of sum it up? Since water is removed.