In the equation \( y = ab^x \), the variable 'a' represents the initial value or the y-intercept of the exponential function when \( x = 0 \). This means that when you plug in 0 for \( x \), the equation simplifies to \( y = a \), indicating that the graph crosses the y-axis at the point \( (0, a) \).
So, the correct interpretation of 'a' in this context is:
The variable 'a' represents the y-intercept, which affects where the graph crosses the y-axis.
The growth rate is determined by the base \( b \). If \( b > 1 \), the function represents exponential growth; if \( 0 < b < 1 \), it represents exponential decay. The steepness of the graph is influenced by the value of \( b \), rather than 'a'.