Identify the type of function represented byf(x) = 4 • 2x.A.Exponential decayB.Increasing linearC.Exponential growthD.Decreasing linearSUBMITarrow_backPREVIOUS

Break Down the Problem

1. Identify the function: $f(x) = 4 \cdot 2^x$.
2. Determine the characteristics of the function to classify its type.

Relevant Concepts

• Exponential functions take the form $f(x) = a \cdot b^x$, where $a$ is a constant, and $b$ is the base.
• If $b > 1$, the function exhibits exponential growth; if $0 < b < 1$, it exhibits exponential decay.

Analysis and Detail

1. In the function $f(x) = 4 \cdot 2^x$:
   • The base $b = 2$ is greater than 1.
   • Therefore, the function increases as $x$ increases, which is characteristic of exponential growth.

Verify and Summarize

1. Since $f(x)$ multiplies by a factor greater than 1 for every unit increase in $x$, this confirms that the function is indeed exponential growth.

Final Answer

The type of function represented by $f(x) = 4 \cdot 2^x$ is C. Exponential growth.