which is the graph of f(x) = 0.5(4)^x?
which is the graph of f(x) = 0.5(4)^x?
Answer
Explanation:
Step1: Identify the form of the function
The function $f(x)=0.5(4)^{x}$ is an exponential - growth function of the form $y = ab^{x}$, where $a = 0.5$ and $b=4>1$.
Step2: Find the y - intercept
When $x = 0$, $f(0)=0.5(4)^{0}=0.5\times1 = 0.5$.
Step3: Analyze the growth behavior
As $x$ increases, since $b = 4>1$, the function value $y$ will increase rapidly. For example, when $x = 1$, $f(1)=0.5\times4=2$; when $x = 2$, $f(2)=0.5\times4^{2}=0.5\times16 = 8$; when $x = 3$, $f(3)=0.5\times4^{3}=0.5\times64 = 32$.
Answer:
The given graph is the correct graph of the function $f(x)=0.5(4)^{x}$ as it has a y - intercept close to $0.5$ and shows rapid growth as $x$ increases.