Understanding Exponential Decay Functions: Explaining the Math Behind Decay and its Applications.

Exponential Decay Function

An exponential decay function is a mathematical function that describes the decrease in value of an exponential quantity over time

An exponential decay function is a mathematical function that describes the decrease in value of an exponential quantity over time. The general form of an exponential decay function is:

y = a * (1 – r)^x

Where:
– y represents the value of the quantity at a given time
– a represents the initial value of the quantity
– r is the decay rate (a value between 0 and 1)
– x represents the time elapsed

The function (1 – r)^x represents the decay factor. As time increases (x), the decay factor decreases, causing the value of y to decrease as well.

To better understand exponential decay functions, let’s consider an example:

Suppose a radioactive substance has an initial mass of 100 grams and its decay rate is 0.05 (5%). We can model the decay of the substance using the exponential decay function:

y = 100 * (1 – 0.05)^x

Let’s calculate the value of the substance after different periods of time:

– After 1 hour (x = 1):

y = 100 * (0.95)^1
= 95 grams

– After 2 hours (x = 2):

y = 100 * (0.95)^2
= 90.25 grams

– After 3 hours (x = 3):

y = 100 * (0.95)^3
= 85.74 grams

As you can see, the value of the substance decreases exponentially over time.

Some important things to note about exponential decay functions:
1. The value of ‘a’ represents the initial value or starting point of the decay.
2. The value of ‘r’ determines the rate at which the decay occurs. The closer ‘r’ is to 1, the slower the decay.
3. The exponent ‘x’ represents the time elapsed since the decay started.

Exponential decay functions are commonly used in various fields such as radioactive decay, population growth, and finance. Understanding how to model and analyze exponential decay can be useful for solving real-world problems.

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