Mathematical Principles Flashcards
Define exponential
A condition where the RATE OF CHANGE or a VARIABLE at any point in time
is PROPORTIONAL to the value of the variable at the time.
What is Eulers number?
Represents the numerical value of 2.718 and is the base of natural logarithms.
Represented by the symbol āeā
What is a logarithm?
The power (x) to which a base must be raised in order to produce the number given as for the equation, x = log_base_(number). The base can be any number 10, 2 , e.
What is the half life?
The time taken for the value of an exponential function to decrease by half, and is represented by the symbol t = 0.5t
What is a time constant?
The time it would have taken for a negative exponential process to complete, had the initial rate of change be maintained throughout.
Time taken for value of an exponential to fall to 37% of its previous value.
Exponential process is completed after three time constants, and 94.9% of the process is complete.
What is the rate constant?
the reciprocal of the time constant.
a marker of the rate of change of the exponential process.
Define accuracy
The ability of a measurement device to match the actual value of the quantity being measured.
Define precision
The ability of a measurement device to match the actual value of the quantity being measured.
What is drift?
A fixed deviation from the true value at all points in the measured range. Drift can be corrected by the process of zeroing.
What is hysteresis?
The phenomenon by which a measurement varies from the input value by different degrees depending on whether the input variable is increasing or decreasing in magnitude at that moment in time.
What are the properties of an exponential decay curve?
- PLASMA CONC approaches by never touches the x-axis. Asymptote.
- PROPORTION OF DRUG ELIMINATED per minute is constant, but amount of drug eliminated varies.
- RATE OF DECLINE of plasma drug concentration varies according to the plasma conc present at the time.
- Gradient of the curve is the elimination rate constant k.
What is the equation that represents an exponential function?
C = dC/ dt
drug conc = change in drug conc/ change in time.
Examples of negative exponential curves?
Nitrogen wash out curve
lung volumes during passive expiration
drug washout curves
Examples of exponential growth
Bacterial growth
Drug wash-in curves
Lung volumes during positive pressure ventilation
