## exponentA number that gives the power to which a base is raised. For example, in 3 ^{2}
the base is 3 and the exponent is 2. ## Exponential equationAn equation of the forma
= ^{x}b where a and b are numbers. For example, if
3^{x} = 81 we can solve for x by restating 81
= 9 × 9 = 3 × 3 × 3 × 3, and so x = 4. More
difficult problems are solved using logarithms:
e.g., if 4^{x} = 15, then xlog_{e}4
= log_{e}15. Therefore 1.386x = 2.7081 and x
= 1.9535 (to 4 decimal places). ## Exponential functionA function of the formf(x) =
a where ^{x}x is positive and does not equal 1.
In terms of differential calculus, f '(x) = alog^{x}_{e}a
f(x) = a. ^{x}## Exponential growthSince the value ofa increases considerably with increases
in ^{x}x, the term exponential growth is used loosely in statistics
to refer to the very rapid growth in number of a quantity over a period
of time. More accurately, it refers to an increase which, if plotted against
units of time, would approximate closely to an exponential
curve (the plotting of an exponential function). ## Related categories• ALGEBRA• FUNCTIONS • PROBABILITY AND STATISTICS | |||||

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