Does the function f of x equals 3 times the quantity 1 over 2 end quantity to the x power represent growth or decay? What is the y-intercept of f(x)?

a. Growth; 0 comma one-half
b. Growth; (0, 3)
c. Decay; 0 comma one-half
d. Decay; (0, 3)

1 answer

The function f(x) = 3(1/2)^x represents decay because as x increases, the value of (1/2)^x gets smaller.

To find the y-intercept of f(x), we need to find the value of f(x) when x is equal to 0.

Substituting x = 0 into the function yields f(0) = 3(1/2)^0 = 3(1) = 3.

Therefore, the y-intercept of f(x) is (0, 3).

The correct answer is (d) Decay; (0, 3).