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.

r(t)=

Answer 1

`r(t)=100,000t+600,000`

Explanation:

Let

r ----> the number of readers (y-coordinate or dependent variable)

t ----> the number of years after 2000 (x-coordinate or independent variable)

Remember

2004 ----> represent t=4 years

2014 ----> represent t=14 years

we have the ordered pairs

(4,1,000,000) and (14,2,000,000)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(2,000,000-1,000,000)/(14-4)`

`m=(1,000,000)/(10)`

`m=100,000(readers)/(year)`

step 2

Find the equation of the line in point slope form

`r-r1=m(t-t1)`

we have

`m=100,000\\point\ (4,1,000,000)`

substitute

`r-1,000,000=100,000(t-4)`

step 3

Convert to slope intercept form

`r=mt+b`

isolate the variable r

`r-1,000,000=100,000t-400,000\\r=100,000t-400,000+1,000,000\\r=100,000t+600,000`

step 4

Convert to function notation

`r(t)=100,000t+600,000`