Question

Easy Algebra Question Help!

Answer 1

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.
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 25
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95


Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.




Between which years will the beaches have approximately the same width?



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

Answer 2

@mtbender74

Answer 3

So there are three questions here...let's look at them one at a time, ok?

Answer 4

ok

Answer 5

For the first one, what do you notice happening to the width of the beaches for one year to the next?

Answer 6

one is increasing and the other is decreasing

Answer 7

which is increasing and which is decreasing?

Answer 8

the first one is decreasing and the second one is increasing

Answer 9

specifically, Western Beach is decreasing and Dunes Beach is increasing?

Answer 10

yes sorry

Answer 11

np :) you just answered the first part

Answer 12

that was easy...let's try the second one

Answer 13

thx :)

Answer 14

at which year number are they *almost* equal in width?

Answer 15

11

Answer 16

right...and at year 11 Western is still wider than Dunes...but then the next year, it switches and Dunes is wider...

what actual year does year 11 represent, if year 0 is 1995?

Answer 17

2006?

Answer 18

haha...everyone always answers with a question :) with confidence :)

2006!

:)

Answer 19

lol

Answer 20

so sometime betwewen years 11 and 12, which is 2006-2007, the beaches were the same width?

Answer 21

possibly

Answer 22

are you unsure, or just hedging your bets?

Answer 23

it could have been but im not 100% sure

Answer 24

we know that Western is continually decreasing in width and Dunes is continually increasing in width...

and in 2006, Western was wider than Dunes...but by 2007, Dunes was wider than Western.

so somewhere between their widths had to be equal...

Answer 25

but I see there is a sequence to the table like they start off at different points but after that western beach is decreasing by 2 and dunes beach is increasing by 5

Answer 26

so would I include that on in the first question too?

Answer 27

you can, but it'll all work out in the thrid question. the rate of change does seem to be even, but the idea is that a) we realize the two are consistently increasing or decreasing. b) at some point their values are equal.

let me show a picture...

Answer 28

oh that helps to understand

Answer 29

Since we know that they started the year with Western larger and ended with Dunes larder, *somewhere* in there they had to meet

Answer 30

the rate of change will be what affects *when* in the year they crossed

Answer 31

ok...so we've now answered question 2. :) we're on fire!

Answer 32

lol XD

Answer 33

so #2 is between year 11 and 12

Answer 34

i'd probably say 2006-2007 instead of the year numbers...that way they see you went the extra step to understand what those year numbers represent

Answer 35

yes but to submit It just to be in case I don't want my teacher taking off points u know what I mean?

Answer 36

as a former teacher, i'd have a hard time believing they would take off for that...beside the question asks "Between which years" not "Between which year numbers"

i think you're safe :)

Answer 37

oh ok lol thx :)

Answer 38

so whats for number 3

Answer 39

so the third question is a bit open-ended...it merely asks "what can you do to get a better time of when they are equal"

it never really asks you to figure it out

Answer 40

yes because after 12 years if theyre constant then they will never meet again

Answer 41

right, but if we wanted to know the month, day, or even hour, in 2006 when they were the same width, what could we do...given the data we have?

Answer 42

well,l you can do pretty much what i did with the picture...graph it and calculate where the lines cross

Answer 43

let's ignore the data before year 11...let's make 2006 year 0 instead...you follow?

Answer 44

yes sir!

Answer 45

alright! new picture...

Answer 46

that's two lines...we can get equations for them, yes?

we can get a solution point for them, yes?