Exponential Growth and Decay Applications

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Future Value = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Depreciation can be calculated using the formula: Value = Initial Value * (1 - rate)^t, where rate is the depreciation rate and t is the time in years.

The decay factor is calculated as (1 - rate). For example, if the rate is 8%, the decay factor is 0.92.

Compounding semiannually means that interest is calculated and added to the principal twice a year.

If the base of the exponential function is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

The interest rate determines how much interest is earned on the principal over time; a higher rate results in more interest accrued.

Total Amount = Principal + Interest, where Interest can be calculated using the compound interest formula.

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has been added.