Does y=4(

2
1

)
x
model exponential growth or decay? How do you know?

The function models decay since the b-value is less than 1 but greater than 0.

The function models growth since the b-value is greater than 1.

The function models growth since the b-value is less than 1 but greater than 0.

The function models decay since the b-value is greater than 1.

1 answer

To determine if the function \( y = 4 \left( \frac{1}{2} \right)^x \) models exponential growth or decay, we need to examine the base \( b \) of the exponential function.

In this case, the base is \( \frac{1}{2} \).

  • If the base \( b \) is greater than 1, the function models exponential growth.
  • If the base \( b \) is between 0 and 1 (i.e., \( 0 < b < 1 \)), the function models exponential decay.

Since \( \frac{1}{2} \) is less than 1 and greater than 0, the function models decay.

Therefore, the correct statement is: The function models decay since the b-value is less than 1 but greater than 0.