Which of the following is a family of exponential curves?
Practice Questions
Q1
Which of the following is a family of exponential curves?
y = e^x
y = x^2
y = log(x)
y = sin(x)
Questions & Step-by-Step Solutions
Which of the following is a family of exponential curves?
Step 1: Understand what an exponential curve is. An exponential curve is a graph of a function where the variable is in the exponent.
Step 2: Recognize the general form of an exponential function, which is y = a^x, where 'a' is a positive number called the base.
Step 3: Identify that the equation y = e^x is a specific case of the general form, where the base 'a' is the mathematical constant 'e' (approximately 2.718).
Step 4: Realize that changing the base 'a' in the general form y = a^x creates different exponential curves, which means there are many curves for different values of 'a'.
Step 5: Conclude that y = e^x is part of a family of exponential curves because it can be generalized to y = a^x for any positive base 'a'.
