Exponent Calculator

Exponent Calculator

This Calculator is designed to help you perform exponentiation calculations with ease. In mathematics, an exponent refers to the number of times a number or base is multiplied by itself.

The calculation is straightforward: given a base (b) and an exponent (n), the expression b^n means 'multiply b by itself n times'.

            For example:
            2^3 = 2 * 2 * 2 = 8
        

What is Exponential Growth

An exponential growth function represents a quantity that grows at a consistent rate. It can be seen in a variety of phenomena, such as population growth, interest compounding, or radioactive decay.

This calculator will calculate the future value A of an investment or population based on an initial value P, growth rate r (expressed as a decimal), and time t (in periods). The formula for exponential growth is A = P * e^(r*t), where e is Euler's number.

The formula for exponential growth is: A = P * e^(rt)

            where:
            - A is the final amount that will be achieved after some time t.
            - P is the initial principal amount.
            - r is the rate of interest.
            - n is the number of times interest applied per time period.
            - t is time
            For example:
        

If you start with $1000 and it grows at 5% per year, after 2 years you will have: 1000 * (1 + 5/100) ^ 2 = $1102.5

What is Exponential Decay

Contrary to exponential growth, exponential decay describes a process that decreases at a rate proportional to the value that it currently has. This behavior can be observed in nature in a multitude of forms like radioactive decay or depreciation.

The formula for exponential decay is: A = P * e^(-rt)

            where:
            - y is the final amount
            - a is the initial amount
            - r is the decay rate (in percent)
            - t is time
            For example:
        

If you start with $1000 and it decays at 5% per year, after 2 years you will have: 1000 * (1 - 5/100) ^ 2 = $902.5