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.

Answer 1

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:

$r = 100000 t + 600000$