What type of curves does the equation y = e^(kx) represent?

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Question: What type of curves does the equation y = e^(kx) represent?

Options:

Correct Answer: Exponential functions

Solution:

The equation y = e^(kx) represents a family of exponential functions with varying growth rates (k).

What type of curves does the equation y = e^(kx) represent?

What type of curves does the equation y = e^(kx) represent?

Step 1: Identify the equation given, which is y = e^(kx).
Step 2: Recognize that 'e' is a constant (approximately 2.718) and is the base of natural logarithms.
Step 3: Understand that 'k' is a variable that can change, affecting the shape of the curve.
Step 4: Note that if k is positive, the curve will rise steeply as x increases (exponential growth).
Step 5: If k is negative, the curve will fall as x increases (exponential decay).
Step 6: Realize that the value of k determines how fast the curve grows or decays.
Step 7: Conclude that y = e^(kx) represents a family of curves that can either grow or decay depending on the value of k.

No concepts available.