Final answer:
An upward trend for an exponential function is called exponential growth. It occurs when a quantity increases at a rate proportional to its current value, often depicted as a 'J-shaped' curve.
Step-by-step explanation:
The term for an upward trend in an exponential function is exponential growth. This concept is crucial in exponential arithmetic, where it describes a situation in which a quantity increases at a rate proportional to its current value. For instance, if we have a population that doubles every period, the scale of growth would follow a pattern of 2, 4, 8, 16, and so on, with each step multiplying by a base of 2. This pattern represents exponential growth, which can also be described by anexponential equation with the population size (P) over time (t) as P(t) = P0ert, where P0 is the initial population size, e is the base of natural logarithms, r is the growth rate, and t is time.
When resources are unlimited, organisms, populations or values in an exponential function can grow in such a manner, which is often depicted as a 'J-shaped' curve on a graph. Scientific notation, also referred to as exponential notation, is related but different; it is a way to express very large or very small numbers using a digit term and an exponential term. For instance, the number 500 can be written in scientific notation as 5 x 102.