In 2004, a magazine’s circulation was about 1,000,000 readers. In 2014, the magazine had about 2,000,000 readers. Write a linear model that

Question

In 2004, a magazine’s circulation was about 1,000,000 readers. In 2014, the magazine had about 2,000,000 readers. Write a linear model that shows the number of readers, r, of the magazine t years after 2000.

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Abigail 1 week 2022-01-12T10:07:00+00:00 1 Answer 0 views 0

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    2022-01-12T10:08:30+00:00

    Answer:

     m= \frac{r_2 -r_1}{t_2 -t_1}= \frac{2000000-1000000}{14-4}=100000

    And then we can use for example the first point  (t_1, r_1) = (4, 1000000) to find the intercept:

     1000000= 100000*4 + b

    b=600000

    So then the linear model for this case should be:

     r = 100000 t + 600000

    Step-by-step explanation:

    For this case we want to find a linear model given by:

     r =mt+b

    Where r = represent the number of readers , t= years after 2000

    m = the slope for the model and b the intercept

    For this case we can define the following points from the data given:

     (t_1, r_1) = (4, 1000000) 4 years after 2000

     (t_2, r_2) = (14, 2000000) 14 years after 2000

    We can find the slope with the following formula:

     m= \frac{r_2 -r_1}{t_2 -t_1}= \frac{2000000-1000000}{14-4}=100000

    And then we can use for example the first point  (t_1, r_1) = (4, 1000000) to find the intercept:

     1000000= 100000*4 + b

    b=600000

    So then the linear model for this case should be:

     r = 100000 t + 600000

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