Question

How do you find the equation of exponential decay?

Answer 1

We start solving the problem by recalling the definition of exponential decay as a quantity undergoing decay (decrease in its numbers) exponentially in the given time ‘t’. We then give a general equation to represent exponential decay by assuming the required variables to get the solution of the given problem.

Complete step-by-step answer:
According to the problem, we are asked to find the equation of exponential decay.
Let us recall the definition of exponential decay.
We know that if a quantity undergoes decay (decrease in its numbers) exponentially to the given time ‘t’, then that growth is known as exponential decay. This is represented as follows:
$\Rightarrow x=a{{b}^{-t}}$.
Where x = quantity of particle at time t.
$\Rightarrow$ a = quantity of particle at time $t=0$.
$\Rightarrow$ b = decay factor.
$\Rightarrow$ t = time.
So, we have found the required equation of the exponential decay as $x=a{{b}^{-t}}$.
$\therefore$ The required equation of the exponential decay is $x=a{{b}^{-t}}$.

Note: Whenever we get this type of problems, we first recall the respective definition and then give an example following that definition. We should not think that $e$ is the only constant that can be used as a growth or decay factor in exponential growth or decay, which is the common mistake done by students. Similarly, we can expect problems to tell the properties to identify whether the given function represents exponential growth.