What is exponential growth in environmental science?
Answers
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function of time is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent. Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay, the function values forming a geometric progression. In either exponential growth or exponential decay, the ratio of the rate of change of the quantity to its current size remains constant over time.
The formula for exponential growth of a variable x at the growth rate r, as time tgoes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is
{\displaystyle x_{t}=x_{0}(1+r)^{t}}