Find the linear function that models the town’s population P as a function of the year, t, where t is the number of years since the model began.

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           2500So 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