Which of the following represents a family of exponential curves?
Practice Questions
Q1
Which of the following represents a family of exponential curves?
y = ae^(bx)
y = ax^2 + bx + c
y = a sin(bx)
y = a log(bx)
Questions & Step-by-Step Solutions
Which of the following represents a family of exponential curves?
Correct Answer: y = ae^(bx)
Step 1: Understand what an exponential curve is. An exponential curve is a graph that shows how a quantity grows or decays at a constant rate.
Step 2: Identify the general form of an exponential equation. The general form is y = ae^(bx), where 'e' is a constant (approximately 2.718).
Step 3: Recognize the variables in the equation. In y = ae^(bx), 'a' and 'b' are constants that can change, which will affect the shape of the curve.
Step 4: Realize that changing 'a' will stretch or compress the curve vertically, while changing 'b' will affect the rate of growth or decay of the curve.
Step 5: Conclude that since 'a' and 'b' can take on different values, the equation y = ae^(bx) represents a family of exponential curves.
