Question #bf489

1 Answer
Mar 1, 2017

Answer:

#y=2x+2#

Explanation:

Observe that:
Difference in each step for advertising is +2
Difference in each step for revenue is +4

Let the advertising signature be #i#
Let the ith advertising signature be #a_i#

#color(blue)("Consider the number structure")#

#a_0->2#
#a_2->6#
#a_4->10#
#a_6->14#
#a_8->18#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We need to relate #i# to revenue. #a_0->(0-2)+4=2#

#color(red)(a_0->-2+4=2)#
#color(red)(a_2->-2+4+4=6)#
#color(red)(a_4->-2+4+4+4=10)#
#color(red)(a_6->-2+4+4+4+4=14)#
#color(red)(a_8->-2+4+4+4+4+4=18)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets try something:

#color(red)(a_0->-2+4=2)#
#color(green)(a_1->-2+4+2=4)#
#color(red)(a_2->-2+4+2+2=6)#
#color(green)(a_2->-2+4+2+2+2=8)#
#color(red)(a_4->-2+4+2+2+2+2=10)#
#color(green)(a_5->-2+4+2+2+2+2+2=12)#
#color(red)(a_6->-2+4+2+2+2+2+2+2=14 )#
#color(green)(a_7->-2+4+2+2+2+2+2+2+2=16)#
#color(red)(a_8->-2+4+2+2+2+2+2+2+2+2=18 )#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the same as:
#a_0->2=2#
#a_1->2+2=4#
#a_2->2+2+2=6#
#a_3->2+2+2+2=8#
#a_4->2+2+2+2+2=10#
#a_5->2+2+2+2+2+2=12#
#a_6->2+2+2+2+2+2+2=14 #
#a_7->2+2+2+2+2+2+2+2=16#
#a_8->2+2+2+2+2+2+2+2+2=18 #

so any #a_i=2(i+1) =2i+2#

As this is linear we use the standardised format #y=mx+c#

Set #i=x# giving: #y=2x+2#

I will let you draw the graph