Exponential growth models apply to any situation where the growth is proportional to the current size of the quantity of interest.
Exponential growth models are often used for real-world situations like interest earned on an investment, human or animal population, bacterial culture growth, etc.
The general exponential growth model is
,
where is the initial amount or number, is the growth rate (for example, a growth rate means ), and is the time elapsed.
Example 1:
A population of with a annual growth rate would be modeled by the equation:
with in years.
Sometimes, you may be given a doubling or tripling rate rather than a growth rate in percent. For example, if you are told that the number of cells in a bacterial culture doubles every hour, then the equation to model the situation would be:
with in hours.
Example 2:
Suppose a culture of bacteria is put into a petri dish and the culture doubles in size every hour. Predict the number of bacteria that will be in the dish after hours.
bacteria