How Does Sugar Inversion Impact Food Preservation Rates?

[tuongcong]

Question:
In the process of preserving food, cane sugar is broken down(called the process of inversion) into 2 simpler sugars: glucose and fructose. In dilute solutions, The inversion rate is proportional to the concentration y(t) of unaltered sugar. If the concentrations 1/50 @ t=0 and 1/200 after 3 hrs, Find the concentrations of unaltered sugar after 6 hrs and after 12hrs.

 

[CaptainZappo]

Think of this problem as a typical half-life scenario. You can either solve it directly with the equations descriptive of half-life, or better yet, you can set up the relationship describing such a process and solve the differential equation.

Hint: the differential equation will be a linear, first order, separable equation.

Question:
In the process of preserving food, cane sugar is broken down(called the process of inversion) into 2 simpler sugars: glucose and fructose. In dilute solutions, The inversion rate is proportional to the concentration y(t) of unaltered sugar. If the concentrations 1/50 @ t=0 and 1/200 after 3 hrs, Find the concentrations of unaltered sugar after 6 hrs and after 12hrs.

 

[tuongcong]

can u be more specific plssssss.
I am totally blind on this problem.

 

[CaptainZappo]

Ok. I will set up the relationship for you and leave the actual solving for you.

Please see the attached Word document for the procedure.

 

[berkeman]

Ok. I will set up the relationship for you and leave the actual solving for you.

Please see the attached Word document for the procedure.

The attachment does not show enough detail to be considered posting a solution, so I approved it. Thanks for being careful to provide tutorial help only, CaptainZappo.