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In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
Rate of change may refer to: Rate of change (mathematics) , either average rate of change or instantaneous rate of change Instantaneous rate of change , rate of change at a given instant in time
Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found. Differentiate both sides of the equation with respect to time (or other rate of change). Often, the chain rule is employed at this step. Substitute the known rates of change and the known quantities into the equation.
The rate of evolution is quantified as the speed of genetic or morphological change in a lineage over a period of time. The speed at which a molecular entity (such as a protein, gene, etc.) evolves is of considerable interest in evolutionary biology since determining the evolutionary rate is the first step in characterizing its evolution. [1]
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation , where N is the quantity and λ ( lambda ) is a positive rate called the exponential decay constant , disintegration constant , [ 1 ] rate constant , [ 2 ] or ...
For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.
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A possible mechanism in two elementary steps that explains the rate equation is: NO 2 + NO 2 → NO + NO 3 (slow step, rate-determining) NO 3 + CO → NO 2 + CO 2 (fast step) In this mechanism the reactive intermediate species NO 3 is formed in the first step with rate r 1 and reacts with CO in the second step with rate r 2.