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Therefore, the mean lifetime is equal to the half-life divided by the natural log of 2, or: = / /. For example, polonium-210 has a half-life of 138 days, and a mean lifetime of 200 days. Solution of the differential equation
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely ...
In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. [1] [note 1] The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to ...
Rate equation. In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only ...
Clearance (pharmacology) In pharmacology, clearance ( ) is a pharmacokinetic parameter representing the efficiency of drug elimination. This is the rate of elimination of a substance divided by its concentration. [1] The parameter also indicates the theoretical volume of plasma from which a substance would be completely removed per unit time.
The number at the top indicates how many half-lives have elapsed. Half-life. A more commonly used parameter is the half-life T 1/2. Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions:
An ordinary differential equation ( ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y ), which, therefore, depends on x. Thus x is often called the independent variable of the equation.
t. e. Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator. and of the integration operator [Note 1] and developing a calculus for such operators generalizing the classical one.