Given the equation y=ab

x
, which of these BEST describes what the variable 'b' represents, and how does it affect the graph?

The variable 'b' represents the growth rate, which affects the steepness.

The variable 'b' represents the growth rate, which affects growth vs. decay.

The variable 'b' represents the y-intercept, which shifts the graph up or down.

The variable 'b' represents the growth rate, which affects the steepness and growth vs. decay.

1 answer

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.