Write a deferential equation describing the given situation.
The rate at which the concentration of a drug in the bloodstream decreases is proportional to the concentration. Let Q(t) be the concentration of the drug at any time t and k be a positive constant.
dQ/dt = ?
THANKS!!!
dQ/dt = kQ (if you please)
To write the differential equation describing the given situation, we need to express the relationship between the rate of change of drug concentration (dQ/dt) and the drug concentration (Q).
According to the given information, the rate at which the concentration decreases is proportional to the concentration itself. This means that as the concentration decreases, the rate of change also decreases proportionally.
Let's consider this proportionality constant as k (positive constant).
Therefore, we can write the differential equation as:
dQ/dt = -kQ
Explanation of how to obtain the answer:
To arrive at the differential equation, we use the information given in the question that the rate of change of the drug concentration is proportional to the concentration itself. We express this relationship using a proportionality constant (k).
By convention, when expressing rates of change, it is common to use the notation dQ/dt, where dQ represents the infinitesimal change in the drug concentration (Q) over an infinitesimally small time interval dt.
The negative sign (-) is included in the equation because the concentration is decreasing, meaning the rate of change will be negative.
Hence, the resulting differential equation is dQ/dt = -kQ.