Identify the family of curves represented by the equation y = e^(kx).

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Question: Identify the family of curves represented by the equation y = e^(kx).

Options:

Correct Answer: Exponential functions

Solution:

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

Identify the family of curves represented by the equation y = e^(kx).

Identify the family of curves represented by the equation y = e^(kx).

Step 1: Understand the equation y = e^(kx). This means y is equal to the exponential function e raised to the power of k times x.
Step 2: Recognize that 'e' is a constant (approximately 2.718) that is the base of natural logarithms.
Step 3: Identify 'k' as a variable that can change. It determines how quickly the function grows or decays.
Step 4: Realize that different values of 'k' will create different curves. For example, if k is positive, the curve will grow upwards; if k is negative, the curve will decrease.
Step 5: Conclude that all these curves (for different values of k) form a family of exponential functions.

Exponential Functions – The equation y = e^(kx) represents exponential functions where 'k' determines the growth rate.