Which of the following equations represents an exponential function? A. y = 3x^2 B. y = 3(2^x) C. y = 2x^3 D. y = 5x + 4
Understand the Problem
The question asks to identify which of the given equations represents an exponential function. An exponential function has the form y = a*b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.
Answer
B. $y = 3(2^x)$
Answer for screen readers
B. $y = 3(2^x)$
Steps to Solve
- Analyze option A: $y = 3x^2$
This is a quadratic function because the variable $x$ is raised to the power of 2. It does not fit the form of an exponential function.
- Analyze option B: $y = 3(2^x)$
This equation has the form $y = a \cdot b^x$, where $a = 3$ and $b = 2$. The variable $x$ is in the exponent, which is the defining characteristic of an exponential function.
- Analyze option C: $y = 2x^3$
This is a polynomial function, specifically a cubic function, because the variable $x$ is raised to the power of 3 which is a constant. It does not fit the form of an exponential function.
- Analyze option D: $y = 5x + 4$
This is a linear function because the variable $x$ is raised to the power of 1. It does not fit the form of an exponential function.
- Identify the exponential function
Based on the analysis above, only option B, $y = 3(2^x)$, represents an exponential function.
B. $y = 3(2^x)$
More Information
Exponential functions are used to model many real-world phenomena, such as population growth, radioactive decay, and compound interest.
Tips
A common mistake is confusing exponential functions with polynomial functions. In an exponential function, the variable is in the exponent, while in a polynomial function, the variable is the base.
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