personal income (in 1998 dollars) in one state increased approx linearly from $20,808 in 1998 to $22,395 in 2003. personal income (in 1998 dollars) in the other state increased approx linearly from $26,155 in 1998 to $26,508 in 2003.

a) let f(t) be personal income (in 1998 dollars) in one state and g(t) be personal income (in 1998 dollars) in the other state, both in the year that is t years since 1998.Find the equation of f and g.

Question

personal income (in 1998 dollars) in one state increased approx linearly from $20,808 in 1998 to $22,395 in 2003. personal income (in 1998 dollars) in the other state increased approx linearly from $26,155 in 1998 to $26,508 in 2003.

a) let f(t) be personal income (in 1998 dollars) in one state and g(t) be personal income (in 1998 dollars) in the other state, both in the year that is t years since 1998.Find the equation of f and g.

anonymous · Answer

Alright, so we have two points for f(t). The points are (0,20808) and (5,22395). The same with g(t); points (0,26155) and (0,26508). Do you understand this part?

anonymous · Answer

yes

anonymous · Answer

We know they are approximately linear. Therefore, we can right them as the first degree function f(x)=mx+b, where m is the slope, and b is the y-intercept--the y value when x=0. Slope can be found via the change in y over the change in x. In five years, how much money has accrued?

anonymous · Answer

i need both the f(t) and g(t) in an equation to do the substitution or elimination method

anonymous · Answer

and while figuring out the problem b is an outrageous number

anonymous · Answer

They're giving you outrageous numbers, so you should only expect outrageous numbers when you do math on them. ;D

anonymous · Answer

lol

anonymous · Answer

i did y-y1=m(x-x1)

anonymous · Answer

Alright, let me condense my hints. You're given two points for f(t) and g(t) each. Two points, (x1,y1), and (x2,y2). In this case, x1 is always x1=0, since the time t starts counting at the earliest year given.

We know the form y=mx+b. m can be found a la (y2-y1)/(x2-x1), but remember x1 is 0. b can be found at f(0) or g(0), which we're already given; y1 for both cases.

I'm sorry, but I'm not giving a direct answer. Knowing the method, and being careful with calculations, should be more than sufficient.

anonymous · Answer

it would be 22395-20808/5=317.4 f(t)
26508-26155/5= 70.6

anonymous · Answer

i got that part but when i plug it in to the equation it turns out to be this y-20808=317.4(x-0) right?

anonymous · Answer

Yeah, I think that works out right. Nicely done.

anonymous · Answer

when i multiply 317.4*20808 =6604459.2

anonymous · Answer

is that right for the equation?