Dilution Problem (Probably Separable)
So I'm doing this problem 3 on page 125 of Tenenbaum's ODE and I'm not getting the same answer, not sure why.
It says, suppose you have a tank of 100 gallons of water with 30 lbs of salt, evenly diluted, and 3 gallons are drained per minute while four gallons of fresh water are fed in each minute while constant stirring ensures homogeneity of the fluid's salt content. What is the amount of salt contained after 10 minutes?
I figure are total quantity of salt and time respectively so since will represent the number of gallons of fluid leaving in minutes, and the quantity of salt per gallon. If that were so, though, when I separate variables and integrate, I wouldn't have any logarithmic functions in my equation, whereas the answer given in the book has an exponential.