exponential A mathematical function that varies as the power of a particular quantity (i.e. a rate of change (increase or decrease) that is calculated as a fixed percentage of the starting value and, therefore, in which the logarithms of a value change linearly in any given period of time). The amount of change in a particular period is calculated as the starting value plus the interest accrued in preceding periods, multiplied by the rate of change (e.g. for a quantity, starting at 100, that grows exponentially by 10 per cent in each unit of time: 100, 110 (100 + 10 per cent of 100), 121 (110 + 10 per cent of 110), 132.1 (121 + 10 per cent of 121),…). Fears have been expressed (e.g. by some environmentalists) that the size of the human population may increase exponentially and the demands such growth imposes on essential resources may cause stocks of these to be depleted exponentially. In biological (and economic) systems, however, exponential rates of change are never sustained (see J-shaped growth curve and S-shaped growth curve).

ex·po·nen·tial / ˌekspəˈnenchəl/ • adj. Math. of or expressed by a mathematical exponent: an exponential curve. ∎  (of an increase) becoming more and more rapid: the budget was rising at an exponential rate.DERIVATIVES: ex·po·nen·tial·ly adv.

exponential Applied to a rate of change (increase or decrease) that is calculated as a fixed percentage of the starting value, so that the amount of change in a particular period is calculated as the starting value plus the interest accrued in preceding periods, multiplied by the rate of change.

exponential In general, a function of x of the form ax, where a is a constant. The exponential function ex′ where e is the base of natural logarithms, 2.7182818…, can be represented by a power series 1 + x + x2/2! + x3/3! +….