A(t)=Pe^rt
The equation A(t)=Pe^rt is an exponential growth/decay model commonly used in mathematics and science
The equation A(t)=Pe^rt is an exponential growth/decay model commonly used in mathematics and science. Let’s break down the different components of the equation:
– A(t): This represents the amount or quantity at a specific time t. It could be the population of a city, the value of an investment, or any other measurable quantity.
– P: This is the initial amount or value at time t=0. It is the starting point or the value of A(0).
– e: This is the mathematical constant known as Euler’s number, approximately equal to 2.71828. It is an irrational number, similar to pi.
– r: This represents the growth/decay rate per unit of time. It could be a positive or negative value, depending on whether we have exponential growth or decay. A positive value represents growth, while a negative value represents decay.
– t: This is the time variable. It represents the specific point in time where we want to calculate the value of A(t).
When you plug in specific values for P, r, and t into the equation, it allows you to find the value of A(t) at that particular time. This formula is particularly useful in situations where the rate of growth/decay is continuously compounded, such as exponential population growth or compound interest.
To use this equation, you need to know the initial amount, growth/decay rate, and the specific time you want to calculate the value for.
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