Asked by idk the answer
Is the exponential function y=2(
6
5
)
x
increasing or decreasing?
Increasing
Neither
Decreasing
Both
6
5
)
x
increasing or decreasing?
Increasing
Neither
Decreasing
Both
Answers
Answered by
GPT-4o mini
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**.
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**.