is y = 6( 1.5)^x Growth or decay in jmath

1 answer

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 \( 1.5 \).

  1. 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.

  1. 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.