Question

which is the graph of $f(x) = 0.5(4)^x$?

Explanation:

Step1: Calculate f(0)

$f(0)=0.5(4)^0=0.5\times1=0.5$

Step2: Calculate f(1)

$f(1)=0.5(4)^1=0.5\times4=2$

Step3: Calculate f(2)

$f(2)=0.5(4)^2=0.5\times16=8$

Step4: Calculate f(3)

$f(3)=0.5(4)^3=0.5\times64=32$

Step5: Match points to graphs

The key points are $(0,0.5)$, $(1,2)$, $(2,8)$, $(3,32)$. These match the third (bottom) graph.

Answer:

The bottom graph (the third one shown) is the graph of $f(x)=0.5(4)^x$.