Question #bf489

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Question #bf489

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Answer 1 · 2017-03-01T22:37:32

$y = 2 x + 2$ $y=2x+2$

Explanation:

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

Let the advertising signature be $i$ $i$
Let the ith advertising signature be $a_{i}$ $a_i$

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

$a_{0} \to 2$ $a_0->2$
$a_{2} \to 6$ $a_2->6$
$a_{4} \to 10$ $a_4->10$
$a_{6} \to 14$ $a_6->14$
$a_{8} \to 18$ $a_8->18$
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We need to relate $i$ $i$ to revenue. $a_{0} \to (0 - 2) + 4 = 2$ $a_0->(0-2)+4=2$

$a_{0} \to - 2 + 4 = 2$ $color(red)(a_0->-2+4=2)$
$a_{2} \to - 2 + 4 + 4 = 6$ $color(red)(a_2->-2+4+4=6)$
$a_{4} \to - 2 + 4 + 4 + 4 = 10$ $color(red)(a_4->-2+4+4+4=10)$
$a_{6} \to - 2 + 4 + 4 + 4 + 4 = 14$ $color(red)(a_6->-2+4+4+4+4=14)$
$a_{8} \to - 2 + 4 + 4 + 4 + 4 + 4 = 18$ $color(red)(a_8->-2+4+4+4+4+4=18)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets try something:

$a_{0} \to - 2 + 4 = 2$ $color(red)(a_0->-2+4=2)$
$a_{1} \to - 2 + 4 + 2 = 4$ $color(green)(a_1->-2+4+2=4)$
$a_{2} \to - 2 + 4 + 2 + 2 = 6$ $color(red)(a_2->-2+4+2+2=6)$
$a_{2} \to - 2 + 4 + 2 + 2 + 2 = 8$ $color(green)(a_2->-2+4+2+2+2=8)$
$a_{4} \to - 2 + 4 + 2 + 2 + 2 + 2 = 10$ $color(red)(a_4->-2+4+2+2+2+2=10)$
$a_{5} \to - 2 + 4 + 2 + 2 + 2 + 2 + 2 = 12$ $color(green)(a_5->-2+4+2+2+2+2+2=12)$
$a_{6} \to - 2 + 4 + 2 + 2 + 2 + 2 + 2 + 2 = 14$ $color(red)(a_6->-2+4+2+2+2+2+2+2=14 )$
$a_{7} \to - 2 + 4 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16$ $color(green)(a_7->-2+4+2+2+2+2+2+2+2=16)$
$a_{8} \to - 2 + 4 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18$ $color(red)(a_8->-2+4+2+2+2+2+2+2+2+2=18 )$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the same as:
$a_{0} \to 2 = 2$ $a_0->2=2$
$a_{1} \to 2 + 2 = 4$ $a_1->2+2=4$
$a_{2} \to 2 + 2 + 2 = 6$ $a_2->2+2+2=6$
$a_{3} \to 2 + 2 + 2 + 2 = 8$ $a_3->2+2+2+2=8$
$a_{4} \to 2 + 2 + 2 + 2 + 2 = 10$ $a_4->2+2+2+2+2=10$
$a_{5} \to 2 + 2 + 2 + 2 + 2 + 2 = 12$ $a_5->2+2+2+2+2+2=12$
$a_{6} \to 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14$ $a_6->2+2+2+2+2+2+2=14$
$a_{7} \to 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16$ $a_7->2+2+2+2+2+2+2+2=16$
$a_{8} \to 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18$ $a_8->2+2+2+2+2+2+2+2+2=18$

so any $a_{i} = 2 (i + 1) = 2 i + 2$ $a_i=2(i+1) =2i+2$

As this is linear we use the standardised format $y = m x + c$ $y=mx+c$

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

I will let you draw the graph

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Question #bf489

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