Question

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.

Answer 1

Need a refresher.. Don't really remember how to solve this one.

Answer 2

@freckles

Answer 3

@Nnesha

Answer 4

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?

Answer 5

Not a clue.

Answer 6

well it is the very next year and we are given the percentage decreases by 0.016 per year

Answer 7

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)

Answer 8

I thought for this problem I have to do the f(x1)- f(x2) thing

Answer 9

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

Answer 10

you are actually given the rate which is -0.016

Answer 11

y=-0.016x+b
you just need to find b now

Answer 12

Um okay? Then I have absolutely no clue how to solve this. I have no examples. And this is the unit review.

Answer 13

well did you understand at t=0 we have .51?

Answer 14

No because I don't get what "t" stands for..

Answer 15

t is the time

Answer 16

in years

Answer 17

after 2000

Answer 18

Oh..

Answer 19

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

Answer 20

or I used t for time variable so t=0

Answer 21

Okay

Answer 22

(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

Answer 23

so you have two points
(0,.51)
(1,.494)

Answer 24

you could even do more points if you wanted to

Answer 25

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

Answer 26

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)

Answer 27

(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

Answer 28

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

Answer 29

Okay. So the answer is p(x)= -0.016x +.51

Answer 30

yes

Answer 31

Okay thanks.

Answer 32

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?

Answer 33

I understand it now.

Answer 34

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

Answer 35

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

Answer 36

Alright. Thank you. Sorry this was my second to last question and I just want to be done. I've been up since 7.

Answer 37

The answer was incorrect. The correct answer is -1.6x+51