00:01
Find the amount of salts in the tank at any time t.
00:04
So for part a, we want to find our change in rate of our salts in our tank.
00:09
That's our dx, dt, which is just our three gallons per minute minus 0 .03x.
00:16
But we can rewrite this as dxdt plus 0 .03x is equal to 3.
00:24
Now we have another expression, or we can find the value of this expression.
00:31
Our expression is going to be e to the integral of 0 .03 dt, we should just e to the 0 .03 times t.
00:42
Now our solution for this integral, x at e to the 0 .03t is equal to the integral from of 3e to the 0 .03t.
00:54
So from this, we get x is equal to 100 plus c .e to the 3e to the 0 .03t dt.
00:58
So from this, we get x is equal to 100 plus c .e to the 3e to 3e to 3e to 3t...