Answer:
16.4 million viewers
Step-by-step explanation:
The number of viewers increased by 8 million from 10 to 18 million when the number of ads increased by 10 ads from 15 to 25. If 23 ads are run, that represents an increase of 8 ads from 15, so we expect 8/10 of the increase in viewers.
8/10 × 8 million = 6.4 million
The number we expect with 23 ads is 6.4 million more viewers than 10 million viewers, so is 16.4 million.
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Alternate solution
We can write a linear equation in 2-point form for the number of viewers expected for a given number of ads:
y = (18 -10)/(25 -15)(x -15) +10
y = (8/10)(x -15) +10
y = 0.8x -2 . . . . . million viewers for x ads
For 23 ads, this gives ...
y = 0.8×23 -2 = 18.4 -2 = 16.4 . . . . million viewers, as above
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Comment on 8/10
I consider it coincidence that the number 23 is 8/10 of the difference between 25 and 15, and the slope of the line is 8/10. The point we're trying to interpolate has no relationship to the slope of the line, and vice versa.
Linear interpolation illustrates the use of linear equation of several points
The number of viewers is 16.4 million, if a 23 one-minute ads runs on Friday.
Linear interpolation is represented as:
[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]
Let:
[tex]x \to[/tex] Time
[tex]y \to[/tex] Viewers
So, we have:
[tex](x_1,y_1) = (15,10m)[/tex]
[tex](x_2,y_2) = (25,18m)[/tex]
[tex](x,y) = (23,y)[/tex]
Substitute the above points in:
[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]
So, we have:
[tex]\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}[/tex]
[tex]\frac{18m - 10m}{25 -15} = \frac{y - 10m}{23 -15}[/tex]
[tex]\frac{8m}{10} = \frac{y - 10m}{8}[/tex]
Multiply both sides by 8
[tex]\frac{64m}{10} = y - 10m[/tex]
[tex]6.4m = y - 10m[/tex]
Collect like terms
[tex]y =10m + 6.4m[/tex]
[tex]y =16.4m[/tex]
Hence, the number of viewers is 16.4 million, if a 23 one-minute ads runs on Friday.
Read more about linear interpolation at:
https://brainly.com/question/4248868
