# Setting up differential equations: 2 problems:

#### Iphoton

##### New member
I'm in Calc 2 and we are in an introduction to differential equations. My professor posted practice test questions but didn't provide answers and I want to know if I correct on the first one and how to set up the second one.

[FONT=&quot]A drug is given to a patient using intravenous line. The mixture in the intravenous line flows into the patient at the rate of 100 ml per hour and contains a drug with a concentration of 3 mg/ml. The patient's body eliminates the drug at the rate of 10 (percent) per hour. Assuming the patient has none of the drug in his body initially, how long will it take the drug to reach 50(percent) of its steady state level?
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[FONT=&quot]dM/dt = 100(3) - (m/10)

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[FONT=&quot]So, for this problem I was having difficulties understanding how to represent the outflow.
usually the format for these equations is: dM/dt = in flow - out flow
out flow = 10% / hr
so:
does this mean m/10 (amount of solution /10)
or does this mean (1/10)(dM/dt) ??

2) [/FONT]
A rumor spreads through a group of people at a rate proportional to the product of the number people who have heard the rumor and the number of people who have not heard the rumor.
Write down
the initial value problem whose solution will be the number of people who have heard the rumor as a function of time if 100 people in a group of 1000 people currently have heard the rumor.

dR/dt = k(heard)(haven't heard)
dR/dt = k(100?)(???)

I need more practice with these kinds of problems. Solving them is the easy part, but setting them up is what I have trouble with.

#### stapel

##### Super Moderator
Staff member
A drug is given to a patient using intravenous line. The mixture in the intravenous line flows into the patient at the rate of 100 ml per hour and contains a drug with a concentration of 3 mg/ml. The patient's body eliminates the drug at the rate of 10 (percent) per hour. Assuming the patient has none of the drug in his body initially, how long will it take the drug to reach 50(percent) of its steady state level?

2) A rumor spreads through a group of people at a rate proportional to the product of the number people who have heard the rumor and the number of people who have not heard the rumor. Write down the initial value problem whose solution will be the number of people who have heard the rumor as a function of time if 100 people in a group of 1000 people currently have heard the rumor.

I need more practice with these kinds of problems. Solving them is the easy part, but setting them up is what I have trouble with.
Then you might want to take a break from homework and try some online study, such as here and here.