4. Match the following function to the description: \( \begin{array}{ll}\text { A. Exponential Growth } & \text { I. } f(n)=3 x^{2} \\ \text { B. Exponential Decay } & \text { II. } h(n)=8+2 n \\ \text { C. Linear } & \text { III. } g(n)=\frac{1}{3} \cdot 8^{n} \\ \text { D. Neither linear nor exponential } & \text { IV. } f(n)=8 \cdot\left(\frac{1}{2}\right)^{n}\end{array} \)

Let's match each function to its corresponding description: 1. **A. Exponential Growth** - **III.** \( g(n) = \frac{1}{3} \cdot 8^{n} \) - This is an exponential function where the base \( 8 \) is greater than 1, indicating exponential growth. 2. **B. Exponential Decay** - **IV.** \( f(n) = 8 \cdot \left(\frac{1}{2}\right)^{n} \) - This is an exponential function with a base \( \frac{1}{2} \) between 0 and 1, indicating exponential decay. 3. **C. Linear** - **II.** \( h(n) = 8 + 2n \) - This is a linear function of the form \( a + bn \), where \( a = 8 \) and \( b = 2 \). 4. **D. Neither linear nor exponential** - **I.** \( f(n) = 3x^{2} \) - This is a quadratic function, which is neither linear nor exponential. **Summary of Matches:** - **A. Exponential Growth** → **III** - **B. Exponential Decay** → **IV** - **C. Linear** → **II** - **D. Neither linear nor exponential** → **I**