Question

A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.

Answer 1

@DanJS

Answer 2

@samanthagreer

Answer 3

Let's tackle the "more than doubled" part first. Please draw a real or imaginary vertical line3 through "Year 14." Estimate, as best you can, what the revenues for that year are for (a) online add revenue and (b) printed ad revenue. Now compare those revenues for Year 14. Does it appear that the revenues for one type of ad are greater than the revenues for the other type of ad? If so, by what factor? Next: Again, look carefully at the graph. Where do the two lines (graphs) intersect? Estimate WHEN that happens (that is, estimate how many years after Year 0 the ad revenues match (are equal).

Answer 4

that is so confusing tbh

Answer 5

Do you want to write an equation for each of those lines? Then solve them for the intersection point. And evaluate them both at year 14, to show that the statement about double is true

Answer 6

yes that makes a lot more sense

Answer 7

Start with the Online Ad Revenue Line...
Two Points on the line
(x,y) = (0,0) and (x1,y1) = (10,3)

Calculate the slope first.

Answer 8

3x/10 is the slope

Answer 9

\[slope = m = \frac{ y - y1 }{ x-x1 } = \frac{ 3-0 }{ 10-0 } = \frac{ 3 }{ 10 }\]

Slope = 3/10
point on line (0,0)

Point-Slope Form

y - 0 = (3/10)*(x - 0)

Equation for Online Ad Revenue
\[y = \frac{ 3 }{ 10 }x\]

Answer 10

no wait 3/10 ok i see that now lol

Answer 11

For the Second Line, Printed Ad Revenue
2 points on the line
(x,y) = (0 , 3) and (x1,y1) = (10 , 2)

Answer 12

\[slope~ m = \frac{ 2-3 }{ 10-0 } = \frac{ -1 }{ 10 }\]

point on line - (0,3)

Point-Slope Equation

y - 3 = (-1/10)*(x - 0)

Equation for the Printed Ad REvenue Line
\[y = \frac{ -1 }{ 10 }x+3\]

Answer 13

Printed Ad Revenue
\[y = \frac{ -1 }{ 10 }x +3\]

Online Ad REvenue
\[y = \frac{ 3 }{ 10 }x\]

Now you can answer the questions

Answer 14

Show what the revenue is for both lines when the year is 14, when x=14.

Answer 15

all i have to do is plug in 14 right?

Answer 16

yes, then show how many times larger the online value is compared to the print value

Answer 17

y=3/100000000000000

Answer 18

is that it :O :O :O

Answer 19

At year 14 (NOW), the revenue from each is,


Online - \[y(14) = \frac{ 3 }{ 10 }*14 = 4.2\]

Print - \[y(14) = \frac{ -1 }{ 10 }*14+3=1.6\]

The online Revenue is currently $4.2 million
The Print Revenue is currently $1.6 million

The online revenue is [4.2 /1.6] = 2.625 times larger than the Print revenue.
He was correct in saying that it is "More than Double"

Answer 20

To find the time when both revenues were equal (intersection point), need to solve...
\[\frac{ 3 }{ 10 }x = \frac{ -1 }{ 10 }x+3\]

x is the time when the revenues from both online and print ad are the same

Answer 21

It turns out that X=7.5

At exactly 7 years and 6 months, both the revenues are the same.

Answer 22

That is how you would solve for the exact values in this problem. It does say just to estimate from the graph. It probably just wanted you to make a good approximation for each value from the graph. But this way is more accurate.

Answer 23

do u mean 5 months??? or 6 @DanJS

Answer 24

x=7.5 (7 and a half years)

Answer 25

half a year is 6 months

Answer 26

duh xD thanks so much

Answer 27

Can i tag u in another question :D