Is the exponential function y=2(

Question

6
5
​
)
x
increasing or decreasing?

Increasing

Neither

Decreasing

Both

Answer 1

To determine whether the function \( y = 2 \left( \frac{6}{5} \right)^x \) is increasing or decreasing, we can analyze the base of the exponential function, which is \( \frac{6}{5} \).

1. Identifying the Base: The base \( \frac{6}{5} \) is greater than 1.

2. Behavior of Exponential Functions:

   • If the base \( b \) of an exponential function \( y = a \cdot b^x \) is greater than 1, then the function is increasing.
   • If the base \( b \) is less than 1, then the function is decreasing.

Since \( \frac{6}{5} > 1 \), the function \( y = 2 \left( \frac{6}{5} \right)^x \) is an increasing function.

Therefore, the answer is Increasing.