Exponential Growth

Exponential Growth refers to a process where the quantity increases at a rate proportional to its current value, resulting in growth that accelerates over time. This type of growth is characterized by the mathematical expression:

N(t) = N_0 * e^(rt)

Where:

• N(t) = the quantity at time t
• N_0 = the initial quantity
• e = the base of the natural logarithm (approximately 2.71828)
• r = the growth rate
• t = time

Examples and Cases:

• Population Growth: A population of bacteria doubles every hour. If you start with 1 bacterium, after 3 hours, you would have 8 (1 → 2 → 4 → 8).
• Investment Returns: If an investment grows at an annual rate of 5%, an initial investment of $100 will grow to approximately $162.89 in 10 years, illustrating the effect of Compound Interest.
• Technology Adoption: The adoption of new technologies, such as smartphones, often follows an exponential growth curve, where the number of users increases rapidly after an initial slow uptake.