The image shows the function $f(n) = 6(2^n)$.

This function is an exponential function, where the output depends on $n$, the exponent applied to the base 2, and then multiplied by 6. As $n$ increases, the function grows exponentially because of the factor $2^n$.

For example:

• When $n = 0$, $f(0) = 6(2^0) = 6(1) = 6$.
• When $n = 1$, $f(1) = 6(2^1) = 6(2) = 12$.
• When $n = 2$, $f(2) = 6(2^2) = 6(4) = 24$.

Would you like further details or specific questions about this function? Here are 5 related questions for further exploration:

1. What is the general behavior of exponential functions compared to linear or polynomial functions?
2. How would you differentiate $f(n) = 6(2^n)$ with respect to $n$?
3. What happens to $f(n)$ as $n \to \infty$?
4. How can this function be applied in real-world contexts, such as population growth or computer science (e.g., binary systems)?
5. Can you express $f(n)$ in terms of logarithms for solving equations involving $n$?

Tip: Exponential growth accelerates rapidly, so functions like $2^n$ grow much faster than polynomial functions as $n$ increases.