For an exponential function g, the value of g(x) decreases by 20% for (May 2023 U.S.)

Correct answer: A) g(x)=16(0.8)^x-2.

Substitute x = 2 into each option.
To solve this problem, we need to find the equation that defines the exponential function g(x) given the information provided.

Given information:
The value of g(x) decreases by 20% for each 1-unit increase in the value of x.
g(2) = 16.
The general form of an exponential function is:
g(x) = a * b^x
where a is the initial value (g(0)) and b is the common ratio (the factor by which the function increases or decreases with each unit change in x).

Since the value of g(x) decreases by 20% for each 1-unit increase in x, the common ratio b must be 0.8 (1 - 0.2 = 0.8).
Now, we can use the given information g(2) = 16 to find the initial value a.

Substituting the values, we get:
g(2) = a * (0.8)^2
16 = a * (0.8)^2
a = 16 / (0.8)^2
a = 16 / 0.64
a = 25

Therefore, the equation that defines the exponential function g(x) is:
g(x) = 25 * (0.8)^x