Does y=

Question

4
3
​
(2)
x
model exponential growth or decay? How do you know?

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

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.

Answer 1

To determine whether the function \( y = \frac{4}{3}(2)^x \) models exponential growth or decay, we need to analyze the base of the exponential function, which is the number 2 in this case.

• Exponential growth occurs when the b-value (the base of the exponent) is greater than 1.
• Exponential decay occurs when the b-value is between 0 and 1.

Here, since the base \( b = 2 \) is greater than 1, the function \( y = \frac{4}{3}(2)^x \) models exponential growth.

So the correct answer is:

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