Final answer:
The exponential decay function for a percentage decay rate of 5% and an initial value of f(0) = 9 is f(x) = 9 × e^(-0.05x).
Step-by-step explanation:
The student is asking for the formula for an exponential function with a decay rate of 5% and an initial value of 9 at x=0. To find this formula, we need to know the general form of the exponential decay function, which is f(x) = a × e(-kx), where a is the initial value, e is the base of the natural logarithm (approximately equal to 2.71828), k is the decay rate, and x is the variable dependent on time.
Given that f(0) = 9 and the decay rate is 5% or 0.05, we can use these values to construct the specific function for this scenario. The formula becomes f(x) = 9 × e(-0.05x). This formula can be used to calculate the value of the function f at any given time x.