The marketing department at cable tv (ctv) wants to know how promotional advertising affects the number of viewers for the saturday night movie. research shows that 10 million viewers watched the movie when ctv ran 15 one-minute ads on friday. when they ran 25 one-minute ads on friday, the movie had 18 million viewers. use linear interpolation to estimate the number of viewers if ctv runs 23 one-minute ads on friday.

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:

Let:

Time

Viewers

So, we have:

Substitute the above points in:

So, we have:

Multiply both sides by 8

Collect like terms

Hence, the number of viewers is 16.4 million, if a 23 one-minute ads runs on Friday.

Read more about linear interpolation at:

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  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.

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

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.

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step-by-step explanation:

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent