Identify the family of curves represented by the equation y = e^(kx).
Practice Questions
Q1
Identify the family of curves represented by the equation y = e^(kx).
Linear functions
Exponential functions
Logarithmic functions
Polynomial functions
Questions & Step-by-Step Solutions
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.
