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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. The most common forms are the ...It is also called the

**exponential****growth****rate**, or the continuous**growth****rate**. Rationale [ edit ] RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period.A double

**exponential function**(red curve) compared to a single**exponential****function**(blue curve). A double**exponential function**is a constant raised to the power of an**exponential****function**. The general formula is (where a >1 and b >1), which grows much more quickly than an**exponential****function**. For example, if a = b = 10:The doubling time is the time it takes for a population to double in size/value. It is applied to population

**growth**, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative**growth****rate**(not the absolute**growth****rate**) is constant ...Logarithmic

**growth**is the inverse of**exponential****growth**and is very slow. A familiar example of logarithmic**growth**is a number, N, in positional notation, which grows as log b (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic. In more advanced mathematics, the partial sums of the harmonic seriesHalf-

**exponential****functions**are used in computational complexity theory for**growth****rates**"intermediate" between polynomial and**exponential**. [2] A**function**grows at least as quickly as some half-**exponential function**(its composition with itself grows exponentially) if it is non-decreasing and , for every . [5]