determine whether the equation could represent exponential growth or decay
y=e^-x
To determine whether the equation y = e^(-x) represents exponential growth or decay, we need to analyze the behavior of the function.
In general, exponential growth occurs when the base of the exponent is greater than 1, while exponential decay occurs when the base of the exponent is between 0 and 1.
For the given equation y = e^(-x), the base of the exponent is e, which is approximately 2.71828. Since e is greater than 1, we can conclude that this equation represents exponential decay.
To further understand this, we can plot the graph of the equation. By substituting different values of x into the equation and calculating the corresponding values of y, we will be able to visualize the behavior of the function.
Let's calculate the values of y for a range of x values:
For x = 0: y = e^(-0) = e^0 = 1
For x = 1: y = e^(-1) ≈ 0.36788
For x = 2: y = e^(-2) ≈ 0.13534
For x = 3: y = e^(-3) ≈ 0.04979
As x increases, y decreases rapidly towards 0. This confirms that the equation y = e^(-x) represents exponential decay.
So, in summary, the equation y = e^(-x) represents exponential decay.