Exponential growth and decay describe how a quantity changes over time at a rate proportional to its current value.

Exponential growth occurs when the rate is positive, leading to a rapid increase over time, like in population growth or compound interest. Exponential decay happens when the rate is negative, causing a rapid decrease, such as in radioactive decay or depreciation of assets.

The fundamental mathematical model is P(t) = P₀ (1 + r)^t, where P(t) is the future value, P₀ is the initial value, r is the growth/decay rate, and t is time. This interactive calculator helps you predict and visualize outcomes in scenarios exhibiting exponential behavior.

• Growth examples: Viral loops, continuous compounding, bacterial population.
• Decay examples: Half-life of substances, fading acoustic waves, car depreciation.