model the relationshio

Question

wihich function models the relationship shown in this table?              x    f(x)

                                                                                                   1   100

                                                                                                    2   50

                                                                                                    3   25

                                                                                                    4   12.5

                                                                                                    5     6.25

 

1. f(x)=100/x                      2.  f(x)=100(1/2)^x

3. f(x)=50(2)^x                   4. f(x)=200(1/2)^x

 

Answer 1

Plug the order pairs of data points into each function to see which one works...

 

(1,100)  

first function f(1) = 100/1 = 100     YES

second function f(1) = 50*2^1 = 50*2 = 100 YES

third function f(1) = 100(1/2)^1 = 100*1/2 = 50   NO. Third function ELIMINATED

fourth function f(1) = 200*(1/2)^1 = 200*1/2 = 100

 

(2,50) 

first function:  f(2) = 100/2 = 50 YES

second function :  f(2) = 50(2^2) = 50*4 = 200 NO. Second function ELIMINATED

fourth function : f(2) = 200(1/2)^2 = 200(1/4) = 50 YES

 

(3,25)

first function f(3) = 100/3 = 33 and 1/3 NO. First function ELIMINATED.

fourth function  is the winner!!!  f(3) = 200(1/2)^3 = 200*1/8 = 25 YES

 

Fourth function: f(4) = 200(1/2)^4 = 200/16 = 100/8 = 50/4 = 25/2 = 12.5

                         f(5) = 200(1/2)^5 = 200/32 = 100/16 = 50/8 = 25/4 = 6.25