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)
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).
To determine whether the function represents growth or decay, we need to analyze the base of the exponential expression.
In this case, the base is 1/2.
If the base is between 0 and 1, then it represents decay. In other words, the function decreases as x increases.
Thus, the function f(x) = 3 * (1/2)^x represents decay.
To find the y-intercept of f(x), we substitute x = 0 into the function and evaluate.
f(0) = 3 * (1/2)^0 = 3 * 1 = 3.
Therefore, the y-intercept of f(x) is (0, 3).
So, the correct answer is d. Decay; (0, 3).