The given function is:
$f(x) = 42.5 \cdot (1.22)^x$

The general form of an exponential function is:
$f(x) = a \cdot b^x$ where $a$ is the initial value and $b$ is the base.

Here:

• $a = 42.5$ (initial value),
• $b = 1.22$ (base of the exponential function).

Completing the statement:

1. The $b$-value is $1.22$.
2. Since $b > 1$, the function represents exponential growth.

Would you like further details on exponential functions or growth models?

Related questions:

1. What happens if the $b$-value is less than 1?
2. How do we determine whether a function represents exponential decay?
3. What is the role of the initial value $a$ in exponential functions?
4. How do exponential functions relate to real-world applications, such as population growth?
5. How can we solve for $x$ in an equation like $42.5 \cdot (1.22)^x = 100$?

Tip: When $b > 1$, exponential growth occurs, and when $0 < b < 1$, exponential decay occurs.