how to write an exponential function for a fractal tree

Question

using the table based on a factral tree how do i write an exponential function.

 

  Step         Number of Branches

 

   0                         1

   1                         2

   2                         4

   3                         8

   4                        16

   5                        32

 

 

 

thanks!

Answer 1

think about a formula that will give you the number of branches for each input, by breaking down the output (number of branches)

 

0    1

1    2=2                =2¹

2    4=2*2             =2²

3    8=2*2*2         =2³

4  16=2*2*2*2      =2⁴

5  32=2*2*2*2*2  = 2⁵

 

Hence a forumla of 2ⁿ will work..

 

y = number of branches

n = step

 

y(n) = 2ⁿ

Answer 2

If we let n= the branch number and N the number of branches then

 

N= 2ⁿ

 

 

Let me know if you have any questions about this

 

Jim Stanton