having trouble with this I have v(t)=100+2t x(t)=10+6t-4t*c(t) c(t)=x(t)/v(t) c(

Question

                    having trouble with this                 

                    
                

                    I have v(t)=100+2t                 

                    x(t)=10+6t-4t*c(t)                 

                    c(t)=x(t)/v(t)                 

                    
                

                    c(30)=.6786                 

                    so...                 

                    x(30)=108.57 pounds                 

                    
                

                    Is this method correct?                 

Initially, a large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is dissolved. Brine containing 0.-5 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Set up a differential equation that describes the weight x(t) (in pounds) of salt in the tank at time t (minutes). Using the given information and the method that you think is most appropriate, solve the initial value problem, i.e. find the function x(t). Find the number of pounds of salt in the tank after 30 minutes.

Explanation / Answer

(i) V(t)=100+2t (correct) x(t)=10+6t-4t*c(t) (incorrect. correct one is the following) => x(t)=10+3t-4t*c(t) C(t)=x(t)/V(t) (correct) (ii)Solving for x(t), x(t) = (10+3t)*(100+4t)/(100+6t) (iii)x(30) = 78.571 pound

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