Answer:
[tex]r(t)=100,000t+600,000[/tex]
Step-by-step 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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{2,000,000-1,000,000}{14-4}[/tex]
[tex]m=\frac{1,000,000}{10}[/tex]
[tex]m=100,000\frac{readers}{year}[/tex]
step 2
Find the equation of the line in point slope form
[tex]r-r1=m(t-t1)[/tex]
we have
[tex]m=100,000\\point\ (4,1,000,000)[/tex]
substitute
[tex]r-1,000,000=100,000(t-4)[/tex]
step 3
Convert to slope intercept form
[tex]r=mt+b[/tex]
isolate the variable r
[tex]r-1,000,000=100,000t-400,000\\r=100,000t-400,000+1,000,000\\r=100,000t+600,000[/tex]
step 4
Convert to function notation
[tex]r(t)=100,000t+600,000[/tex]
