The family of curves defined by the equation y = e^(kx) is classified as:

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Question: The family of curves defined by the equation y = e^(kx) is classified as:

Options:

Correct Answer: Exponential

Solution:

The equation y = e^(kx) represents a family of exponential curves.

The family of curves defined by the equation y = e^(kx) is classified as:

The family of curves defined by the equation y = e^(kx) is classified as:

Step 1: Identify the equation given, which is y = e^(kx).
Step 2: Recognize that 'e' is a constant (approximately 2.718) and 'k' is a variable that can change.
Step 3: Understand that 'x' is the input variable, and as 'x' changes, the value of 'y' will change based on the value of 'k'.
Step 4: Note that the term 'e^(kx)' indicates that the function grows or decays exponentially depending on the value of 'k'.
Step 5: Conclude that since the equation represents a curve that can take different shapes based on 'k', it is classified as a family of exponential curves.

Exponential Functions – The equation y = e^(kx) represents exponential growth or decay depending on the value of k.