Final answer:
The y-intercept (initial value) in the function f(x) = 13(0.2^7x) is 13.
Step-by-step explanation:
The y-intercept, a, in the function f(x) = 13(0.2^7x) represents the value of the function when x = 0. To find the y-intercept, we substitute x = 0 into the function:
f(0) = 13(0.2^7 * 0) = 13(0.2^0) = 13(1) = 13
Therefore, the y-intercept (initial value) of the function is 13.