To determine whether the function \( f(x) = 3 \left( \frac{1}{2} \right)^x \) represents growth or decay, we need to look at the base of the exponential term \(\left( \frac{1}{2} \right)^x\).
- Growth or Decay:
- If the base of the exponential function is greater than 1, the function represents growth.
- If the base is between 0 and 1 (0 < base < 1), the function represents decay.
In this case, the base is \(\frac{1}{2}\), which is less than 1. Therefore, \( f(x) \) represents decay.
- Finding the y-intercept: The y-intercept of a function is found by evaluating the function at \( x = 0 \): \[ f(0) = 3 \left( \frac{1}{2} \right)^0 = 3 \cdot 1 = 3 \]
So the y-intercept is \( (0, 3) \).
Considering both the decay nature and the y-intercept, the correct answer is:
d Decay; (0, 3).