Questions: The function f(x)=3 *(1/2)^x is a decreasing function. True or False

Solution Steps

To determine if the function \( f(x) = 3 \left(\frac{1}{2}\right)^x \) is decreasing, we need to check if the base of the exponential function, \(\frac{1}{2}\), is between 0 and 1. If it is, the function is indeed decreasing.

The function given is \( f(x) = 3 \left(\frac{1}{2}\right)^x \). This is an exponential function of the form \( a \cdot b^x \), where \( a = 3 \) and \( b = \frac{1}{2} \).

For an exponential function \( a \cdot b^x \), the function is decreasing if the base \( b \) satisfies \( 0 < b < 1 \).

In this case, the base \( b = \frac{1}{2} \). We check if \( 0 < \frac{1}{2} < 1 \). Since this inequality holds true, the function is decreasing.

Final Answer