To determine whether the function \( y = 6(1.5)^x \) represents growth or decay, we can look at the base of the exponential term, which is \( 1.5 \).
- Identifying Growth vs. Decay:
- If the base of the exponential function (in the form \( a^x \)) is greater than 1, the function represents exponential growth.
- If the base is between 0 and 1, the function represents exponential decay.
In your case, the base is \( 1.5 \), which is greater than 1. This indicates that the function represents exponential growth.
- What This Means: The function \( y = 6(1.5)^x \) will increase as \( x \) increases. As \( x \) becomes larger, \( y \) will grow larger due to the multiplication by the base \( 1.5 \).
In conclusion, the function \( y = 6(1.5)^x \) is an example of exponential growth.