A five gallon tank is full of water. We open a spigot so 1 gal. leaves the tank and

introduce a mixture of 1/2 lb. per gal at 1 gal per minute. Assuming the mixture is

well mixed, what’s the concentration at time t?

i did these a while ago but cant seem to remember how to finish them... based on my notes, i know to do something like

dA/dt= concentration in- concentration out

so, dA/dt= 1/2 - A/5, where A is gallons of water in the tank at time t. also, the initial condition is A(0)=5

I could guess where to go from here, but I'd rather have someone help me with the rest of it before i learn it the wrong way myself.

EDIT: just took a stab at it and got A=5/2 + 5/2 e^-1/5t

i still cant remember how i used to do these, so im not sure if thats right..