Need help with a differential equations problem!?

Posted on 2015-10-28 13:17:00 in Math by BEN

A particular chemical reaction experiment requires that there is at least 50 grams of a certain key ingredient in the
reacting mix. This compound is being used up at a rate proportional to its amount. When the reaction is initiated with
350 grams, in 20 minutes the amount present is down to 75 grams.

a. Define the variables and set up the initial value problem that would predict the amount of the compound remaining
after t minutes into the reaction. Solve the problem and determine how long this reaction would run.

b. In the next stage of the experiment, the reaction is initiated in the same way, but this compounded is steadily injected
into the reaction mix at the rate of 10 grams a minutes. Use the proportionality constant you already found above, and set
up the differential equation that would model how this reaction would proceed. Without solving the equation,
determine the amount of the compound at which the reaction stabilizes (the amount stops changing).

c. What is minimum steady injection rate that would guarantee that the reaction stabilizes with at least 50 grams of the
compound always present in the mix?

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