Initially 5 grams of salt are dissolved into 10 liters of water. brine with concentration of salt 5 grams per liter is added at a rate of 3 liters per minute. the tank is well mixed and drained at 3 liters per minute. let xbe the amount of salt, in grams, in the solution after t minutes have elapsed. find a formula for the rate of change in the amount of salt, dx/dt, in terms of the amount of salt in the solution x. dxdt=equation editorequation editorgrams/minutefind a formula for the amount of salt, in grams, after tminutes have elapsed. x(t)=equation editorequation editorgramshow long must the process continue until there are exactly 20 grams of salt in the tank?

Salt flows in at a rate of (5 g/L)*(3 L/min) = 15 g/min.

Salt flows out at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

So the net flow rate of salt, given by in grams, is governed by the differential equation,

which is linear. Move the term to the right side, then multiply both sides by :

Integrate both sides, then solve for :

Since the tank starts with 5 g of salt at time , we have

The time it takes for the tank to hold 20 g of salt is such that

b

step-by-step explanation:

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph