A growth factor in mathematics refers to the rate at which a quantity increases over a specific period of time. It is often used in the context of exponential growth, where a particular quantity multiplies by a certain factor in each time interval.
For example, if a population of animals grows by 20% each year, the growth factor would be 1.2. This is because you take the original amount and multiply it by 1 plus the growth rate (expressed as a decimal). In this case, 20% is 0.20, making the growth factor 1 + 0.20 = 1.2.
In mathematical terms, if P is the initial quantity and r is the growth rate expressed as a decimal, the formula for the quantity after t time periods can be expressed as:
P(t) = P(0) × (growth factor)^t
Understanding growth factors is crucial in various fields such as finance, biology, and environmental science, as it helps predict future growth based on current trends.