Question

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

Explanation:

Step1: Calculate f(0)

$f(0)=0.5(4)^0=0.5(1)=0.5$

Step2: Calculate f(1)

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

Step3: Calculate f(2)

$f(2)=0.5(4)^2=0.5(16)=8$

Step4: Calculate f(3)

$f(3)=0.5(4)^3=0.5(64)=32$

Step5: Match points to graphs

Check which graph passes through $(0,0.5)$, $(1,2)$, $(2,8)$, $(3,32)$: this is the bottom graph (the third one, with the circle next to it).

Answer:

The correct graph is the bottom (third) one, which passes through the points $(0, 0.5)$, $(1, 2)$, $(2, 8)$, and $(3, 32)$.