In 2000, 51% of the residents in a large city regularly used newspapers for getting news and this has decrease at an average rate of approximately 1.6% per year since then. Find a linear function in slope- inter form that models this description. The function should model the percentage of residents, P(x), who regularly used the newspaper outlet x years after 2000.

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In 2000, 51% of the residents in a large city regularly used newspapers for getting news and this has decrease at an average rate of approximately 1.6% per year since then. Find a linear function in slope- inter form that models this description. The function should model the percentage of residents, P(x), who regularly used the newspaper outlet x years after 2000.

Mathematics
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So at t=0 we have the year 2000 and we are given at t=0 the percentage was 51% or .51 we are also given the percentage decreases per year by 1.6% aka 0.016 So at t=1 aka year 2001 what would be the new percentage?
Not a clue.
well it is the very next year and we are given the percentage decreases by 0.016 per year
so since at t=0 we had y=.51 then at t=1 we have y=.51-0.016 since this is the very next year the next year after that t=2 we would have y=.51-2(0.016)
I thought for this problem I have to do the f(x1)- f(x2) thing
for this problem they are asking you to find the line that represents the information the line being of the form y=mx+b where m is the rate aka slope and b is the y-intercept
you are actually given the rate which is -0.016
y=-0.016x+b you just need to find b now
Um okay? Then I have absolutely no clue how to solve this. I have no examples. And this is the unit review.
well did you understand at t=0 we have .51?
No because I don't get what "t" stands for..
t is the time
in years
after 2000
Oh..
and since I'm looking at the year 2000 and the question says find an equation for t years after 2000 then then year 2000 is actually when time=0
or I used t for time variable so t=0
Okay
(0,.51) is the first point on the graph (1,.51-.016) is the next point on the graph because we are given the rate of decrease is .016 do you understand this part? In year 2001, the very next year after 2000 we will have a decrease of 0.016 from .51 which is actually .494
so you have two points (0,.51) (1,.494)
you could even do more points if you wanted to
the 2nd year you would have another decrease of 0.016 so (2,.51-2(0.016)) or you could do it from the previous year (2,.494-.016) same number for y whatever strikes your fancy the cool think about recognizing it is (2,.51-2(0.016)) is that you have already noticed your line
for example if you have noticed for the 2nd your the y-coordinate was .51-2(0.016) then you might notice for xth year you have .51-x(0.016)
(x,.51-x(0.016)) which tells you the line is y=.51-x(0.016) or if you prefer to write as y=-0.016x+.51
the question gave you the y-intercept which was the initial percentage and it also gave you the rate you just needed to plug the numbers in
Okay. So the answer is p(x)= -0.016x +.51
yes
Okay thanks.
np I hope it makes sense though.. if you don't like those ugly decimal numbers it might be easier first to look at this example: Say we pick a year and call it t=0. And we are given at t=0 we have 1001 dogs. And we are also given we gain 5 dogs per year. Then for t=1 we have how many dogs?
I understand it now.
ok cool for my example the slope would be positive since we are gaining dogs and not losing dogs :) I didn't want to pick a sad example
if you wanted to know for my example the answer to my question would be 1001+5 or 1006 and if you wanted the equation of the line then it would be y=5x+1001 where y represents the number of dogs and x presents the years after whatever year t=0 represented
Alright. Thank you. Sorry this was my second to last question and I just want to be done. I've been up since 7.
The answer was incorrect. The correct answer is -1.6x+51

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