Identify the family of curves represented by the equation y = e^(kx), where k is a constant.
Practice Questions
1 question
Q1
Identify the family of curves represented by the equation y = e^(kx), where k is a constant.
Linear functions
Exponential functions
Logarithmic functions
Polynomial functions
The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by k.
Questions & Step-by-step Solutions
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Q
Q: Identify the family of curves represented by the equation y = e^(kx), where k is a constant.
Solution: The equation y = e^(kx) represents a family of exponential functions with varying growth rates determined by k.
Steps: 5
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 'k' is a constant. This means it can be any fixed number, like 1, 2, -1, etc.
Step 3: Realize that changing the value of 'k' will change the shape of the curve. For example, if k is positive, the curve will grow upwards; if k is negative, the curve will decrease.
Step 4: Note that all curves represented by this equation are exponential functions, which means they grow or decay at a rate proportional to their current value.
Step 5: Conclude that the family of curves is defined by the different values of 'k', leading to different exponential growth or decay rates.
