A 400gallon cylindrical tank is filled with water When a val

A 400-gallon cylindrical tank is filled with water. When a valve at the bottom of the tank is opened, the flow rate q (in gallons per minute) through the valve is: q(t) = 80e^-0.2t where t is the time in minutes. Knowing that the total amount of water through the valve at any time is the integral of this function, use MAT-LAB to determine: the amount of time required to empty half of the water from the tank the amount of water left in the tank after 15 minutes

Solution

syms t
k=int(80*exp(-0.2*t))

k =

-400*exp(-t/5)

1)half of the tank means 200 gallons

200=-400*exp(-t/5)

1=-2*exp(-t/5)

apply both sides log

-(log2)-(t/5)

answer=0.1386hrs

b.

400*exp(-t/5)

here t=15

so

400*exp(-15/5)

ans =

19.9148