Drug Concentration Decay Problem

In summary, a particular drug in a patient's bloodstream decreases at a rate proportional to its concentration with a constant of proportionality of 0.2. If the initial concentration is 10mm/ml, after 12 hours the concentration will be approximately 1.6mm/ml. The equation for this is dC/dt = -kC, where k = 0.2 and time is measured in hours.
  • #1
evilpostingmong
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Homework Statement



The concentration of a particular drug in a patient’s bloodstream declines at a rate proportional
to the concentration, with constant of proportionality k = 0.2 if time is measured in hours. If
the concentration of the drug in the patient’s bloodstream is 10mm/ml (millimoles per milliliter)
shortly after the injections, what will the concentration be 12 hours later?

Homework Equations





The Attempt at a Solution


Just want to know if I set this one up correctly.
dC/dt=-kC
If I didn't, don't be afraid to rip it apart :D.
 
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  • #2
That looks like what the problem is asking for all right.
 
  • #3
Okay, thanks! Then I must've messed up when I integrated it.
 

Related to Drug Concentration Decay Problem

What is a differential equation?

A differential equation is a mathematical equation that relates a function to its derivatives. It describes the relationship between a function and its rate of change.

What is the difference between an ordinary and partial differential equation?

An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. In other words, ordinary differential equations involve derivatives with respect to a single variable, while partial differential equations involve derivatives with respect to multiple variables.

What is the purpose of using differential equations in science?

Differential equations are used in science to model and describe natural phenomena, such as the motion of objects, the growth of populations, and the flow of fluids. They allow us to make predictions and understand complex systems by using mathematical relationships.

What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations, partial differential equations, linear differential equations, and nonlinear differential equations. These types differ in terms of their complexity and the methods used to solve them.

What are some real-world applications of differential equations?

Differential equations are used in many fields, including physics, engineering, economics, and biology. Some examples of real-world applications include modeling the spread of diseases, predicting stock market trends, and designing aircraft and spacecraft trajectories.

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