Question

Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.

Answer 1

@DanJS

Answer 2

ok

Answer 3

Both of the erosion patterns are linear, they both change at a constant rate.

Answer 4

I decided that by testing what the slope was for each one over different time intervals.

Answer 5

You want to do the same thing here as the last problem. Create a line equation using two points from each, (x,y) = (year, width)

Answer 6

Then set them equal, and solve for X, the time when both beaches have the same width.

Answer 7

X will be the number of years after 1995, since year zero is given as the year 1995

Answer 8

yeah, you know how to solve it then?

Answer 9

The year will be between time x=11 and x=12 from looking at the table. Which corresponds to

2006 and 2007

Answer 10

@misty1212 hi can u help finish this?

Answer 11

@jim_thompson5910 Can u help finish this?

Answer 12

im not fully understanding this? @jim_thompson5910

Answer 13

one sec

Answer 14

alright :)

Answer 15

the year of 0 corresponds to 100 in the first column

so we have the point (0,100)

the next row shows us we have the point (5, 90)

Answer 16

what is the slope of the line through (0,100) and (5, 90) ?

Answer 17

do i divide?

Answer 18

at some point, you will

Answer 19

you first subtract the corresponding coordinates in the same order

Answer 20

100/-85?

Answer 21

not quite

Answer 22

no -100/-85

Answer 23

subtract the y coords: 100 - 90 = 10

subtract the x coords: 0 - 5 = -5

notice how I'm subtracting in the same order

Answer 24

divide the differences

(ydiff/xdiff) = 10/(-5) = -2

Answer 25

:D ok makes some sense now

Answer 26

so that would desrvibe the patterns when u write something that has to do with a certain part you are explaining can u write with part (a,b,or c) that it applies

Answer 27

well notice how we have 100 decrease to 90 from year 0 to year 5

so it's decreasing by 2 per year

you can see this clearly when we go from 80 to 78 (year 10 to year 11)

Answer 28

that slope of -2 tells you the rate of change

Answer 29

ok can u wait while i read through what you wrote @jim_thompson5910

Answer 30

ok

Answer 31

oh so the patterns are the average rate of change?

Answer 32

yeah the pattern tells you how much it's increasing or decreasing (so does the avg rate of change)

Answer 33

so B is what that we are looking for?

Answer 34

what do you mean

Answer 35

Between which years will the beaches have approximately the same width? its between year 11 and 12 right @jim_thompson5910

Answer 36

sorry 10 to 11 @jim_thompson5910

Answer 37

you had 11 and 12 correct

somewhere between those years, the two beaches will have the same width

Answer 38

it might help to graph the two functions and see where they cross

Answer 39

and this for c? Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?

Answer 40

if you find the actual functions for each column, you can use algebra to find the exact point in time when the widths are equal

Answer 41

so heres all what i wrote tell me if its right

Answer 42

3.

point 1- (x,y)= (0,100)
point 2- (x,y)= (5,90)

100-90=10
0-5=-5

divide difference (y diff/ x diff) = 10/(-5) = -2

Decreasing by 2 per year.
-2 is the average rate of change.

B. Between year 11 and 12 the beaches will have approximately the same width.

C. If you find the actual functions for each column, you can use the algebraic techniques to find an exact point in time when widths are equal. @jim_thompson5910

Answer 43

yeah something like that

that looks good

Answer 44

:) thanks so so so much :D

Answer 45

Can u help with oneeee more then its over :D @jim_thompson5910

Answer 46

ok