The correct description for the variable 'b' in the equation \( y = ab^x \) is:
The variable 'b' represents the growth rate, which affects the steepness and growth vs. decay.
In this context:
- If \( b > 1 \), the function represents exponential growth, and the graph will steeply rise as \( x \) increases.
- If \( 0 < b < 1 \), the function represents exponential decay, and the graph will decline as \( x \) increases.
- The steepness of the graph is influenced by the value of \( b \); larger values of \( b \) result in a steeper curve.
Thus, 'b' fundamentally determines whether the graph represents growth or decay and how quickly it rises or falls.