Final answer:
To write an exponential decay function given an initial value of 3 and a decay factor of 2/3, the formula is f(x) = 3(¾)^x. This represents how the quantity decays over time.
Step-by-step explanation:
The student has asked how to write a specific exponential decay function with an initial value of 3 and a decay factor of 2/3. According to the general formula for an exponential function, which is f(x) = abx, we can substitute the provided initial value and decay factor into the formula. Here, a is the initial value and b is the base or the decay factor.
The specific exponential decay function is therefore f(x) = 3(¾)x. In this equation, 3 represents the initial amount of the quantity you are measuring, and (¾) is the factor by which this quantity decays over a certain period, which could be time, cycles, or any other unit of measure depending on the context of the problem.