Question

which function represents exponential growth?

\\( f(x) = 3x \\)
\\( f(x) = x^3 \\)
\\( f(x) = x + 3 \\)
\\( f(x) = 3^x \\)

Explanation:

Identify the definition of an exponential growth function

An exponential growth function is of the form \(f(x) = a \cdot b^x\), where \(a > 0\) and \(b > 1\).

Analyze each given option

• \(f(x) = 3x\): This is a linear function.
• \(f(x) = x^3\): This is a cubic (polynomial) function.
• \(f(x) = x + 3\): This is a linear function.
• \(f(x) = 3^x\): This is an exponential function with base \(b = 3 > 1\), representing exponential growth.

Answer:

• (A) \(f(x) = 3x\)
• (B) \(f(x) = x^3\)
• (C) \(f(x) = x + 3\)
• (D) \(f(x) = 3^x\) (Correct answer)