Question

11 which of the following functions represents the data in the table?

n	0	1	2	3	4	…
f(n)	4	8	16	32	64	…

a ( f(n) = 2^n )
b ( f(n) = 4 cdot 2^n )
c ( f(n) = 4^n )
d ( f(n) = 2 cdot 4^n )

Explanation:

Step1: Test option A with n=0

$f(0)=2^0=1
eq 4$

Step2: Test option B with n=0

$f(0)=4 \cdot 2^0=4 \cdot 1=4$

Step3: Test option B with n=1

$f(1)=4 \cdot 2^1=4 \cdot 2=8$

Step4: Test option B with n=2

$f(2)=4 \cdot 2^2=4 \cdot 4=16$

Step5: Test option C with n=1

$f(1)=4^1=4
eq 8$

Step6: Test option D with n=1

$f(1)=2 \cdot 4^1=2 \cdot 4=8$, test n=0: $f(0)=2 \cdot 4^0=2 \cdot 1=2
eq 4$

Answer:

B. $f(n) = 4 \cdot 2^n$