Question

The table below shows the values of f(n) for different values of n:


n 1 2 3 4 5 6
f(n) 1 2 4 16 128 4096


Which recursive function best represents the values shown in the table?
f(1) = 1, f(2) = 2, f(n) = f(n -3) + f(n - 2); n > 2
f(1) = 1, f(2) = 2, f(n) = f(n -3) f(n - 2); n > 2
f(1) = 1, f(2) = 2, f(n) = 2f(n -1) + f(n - 2); n > 2
f(1) = 1, f(2) = 2, f(n) = 2f(n -1) f(n - 2); n > 2

Answer 1

@UnkleRhaukus

Answer 2

powers of two right?

Answer 3

yea (:

Answer 4

we can't know f(n-3) for n=3
because we dont have f(0)

Answer 5

lets check that last option

f(1) = 1,
f(2) = 2,

f(3) = 2f(3 -1) f(3 - 2)
= ?
does this equal 4?

f(4) = 2f(4 -1) f(4 - 2)
= ?
does this equal 16?

Answer 6

the first one no it does not aand the second one does

Answer 7

f(3) = 2f(3 -1) f(3 - 2)
= 2f(2) f(1)
= 2 x 2 x 1
= ?

Answer 8

4 i think

Answer 9

yeah so that fits the table

Answer 10

f(4) = 2f(4 -1) f(4 - 2)
= 2f(3) f(2)
= 2 x 4 x 2
= ?

Answer 11

16

Answer 12

good, lets check then next term

f(5) = 2f(5 -1) f(5 - 2)
= ?

Answer 13

13 i think i may of got that wrong

Answer 14

im not sure tht one but for a crazy answer im going to say 128 is the answer

Answer 15

f(5) = 2f(4) f(3)
= ?

Answer 16

4096

Answer 17

wait no its its 7 right?

Answer 18

we just found f(4)=16 and f(3) =4

Answer 19

oh ok

Answer 20

so f(4) = 16 and f(3)= 4 then i would add 16 and 4 together then i would get 20 is tht correct ?

Answer 21

if we are testing the fourth option

f(n) = 2f(n -1) f(n - 2)

you have to multiply the terms (not add)

Answer 22

omg im srry i meant mutiply not add i would get 64

Answer 23

yeah

f(5) = 2f(4) f(3)
= 2 x 16 x 4
= 2 x 64
=

Answer 24

128

Answer 25

is that the same as f(5) of the table?

Answer 26

yea

Answer 27

goody, what about f(6) ?

Answer 28

yup its 4096

Answer 29

so we have checked the last option and all the points fit,

Answer 30

If we had tried the third option

f(1) = 1,
f(2) = 2,
f(n) = 2f(n -1) + f(n - 2); n > 2

f(3) = 2f(3 -1) + f(3 - 2)
= 2 f(2) + f(1)
= 2 x 2 + 1
= 5

we see if dosen't match up with the table

Answer 31

oh ok so im a little confused tho im looking at my choices of wat the answer could be but its like its not matching

Answer 32

oh wow wait never mine it is the last option im srry im a little air headed today :/

Answer 33

we tried the last option, with f(n) = 2f(n -1) f(n - 2); n > 2
first, and all the points matched the ones on the table

Answer 34

ik but i submitted it and it was the was the last one was correct :D:D