Answer:
The equation is:
[tex]y=2500t+75000[/tex] where t is the number of years satisfying the inequality [tex]0\let\le5[/tex] and y is the population at that time.
Step-by-step explanation:
So it gives us the initial amount 75000; this is what happens at time 0.
So we have the point (0,75000) is on the function's graph.
(0,75000)
(1,77500) -> It goes 2500 per year. So year 1 the population is 75000+2500.
So we have the y-intercept of the line which is (0,75000).
We just need the slope.
Our goal is to put into slope-intercept form: y=mt+b form where m is the slope and b is the y-intercept.
To find the slope, you line up the points vertically and subtract then put 2nd difference over 1st difference.
( 1 , 77500 )
-( 0 , 75000)
------------------------
1 2500
So the slope is 2500/1=2500 which we should have known earlier since the y's are increasing by 2500 while the x's are increasing by 1.
So while t is between 0 and 5 inclusive we have the following equation:
y=2500t+75000
