is y = 3( 1/2) decay or growth in math

1 answer

The equation \( y = 3\left(\frac{1}{2}\right)^x \) represents exponential decay.

In this equation:

  • The base of the exponent is \(\frac{1}{2}\), which is less than 1.
  • When the base of an exponent is between 0 and 1, the function decreases as \( x \) increases, which indicates decay.

As \( x \) increases, \( \left(\frac{1}{2}\right)^x \) will get smaller and approach 0, leading to a decay in the value of \( y \).

So, \( y = 3\left(\frac{1}{2}\right)^x \) describes exponential decay.