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

₹0.0

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

Options:

Correct Answer: Exponential

Solution:

The equation y = e^(kx) represents an exponential function.

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

The family of curves represented 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 the expression e^(kx) means 'e' raised to the power of 'kx'.
Step 4: Note that this type of equation shows how 'y' changes as 'x' changes, which is characteristic of exponential functions.
Step 5: Conclude that since the equation is in the form of y = a^(bx), where 'a' is a constant and 'b' is a variable, it is classified as an exponential function.

Exponential Functions – The equation y = e^(kx) represents a family of exponential functions where 'e' is the base of natural logarithms and 'k' is a constant that affects the growth rate.