Question

I need help please: I have been to a "Live Math Tutor" and I am unable to understand the response given.
A certain mountain has an elevation of 19,649 ft. In 1915, the glacier on this peak covered 4 acres. By 2000 this glacier had melted to only 1 acre.
a) Assume that the glacier melted at a constant rate each year. Find the yearly rate.
b) Use answer from part A to write a linear equation that gives acreage A of this glacier t years past 1915.

I need to know the following:
* the yearly rate of change is ________acres/year?
*what is the acreage of the glacier t years after 1915? A=___

Answer 1

Sorry...made a mistake that last part of the problem should read: What is the equation that gives the acreage of the glacier t years after 1915?

Answer 2

Well, if we consider only the glacier acreage and don't pay attention to the elevation of the mountain, then we can create the linear equation.

Answer 3

ok, I am listening...

Answer 4

Why do we not pay any attention to that? Because we're not asked anything concerning it.

Answer 5

is all confusing to me

Answer 6

I know. But, next time, to help you out, you might want to consider creating a relationship chart such as this:

Answer 7

Often times, for such problems, there will be a relationship between two things. In this case it is Glacier Height vs. Years.

Answer 8

Which can be plotted on an xy plane or chart.

Answer 9

If you have two points on the same line, you can figure out the slope and the equation of the line.

Answer 10

should the yearly rate of change be answered in a fraction such as: 3/86 acres/year?

Answer 11

Do you know how to find the equation of a line given two points on the line?

Answer 12

no I do not

Answer 13

I have been working on this same problem off & on since yesterday...I am trying

Answer 14

Well, if given two points, you can use the slope formula to find the slope or rate of increase /decrease of a line or relationship between two variables.

Answer 15

\[m = \frac{y - y_1}{x - x_1}\]

Answer 16

\[m =\frac{4 - 1}{1915 - 2000} = -\frac{3}{85}\]

Answer 17

looking, trying 2 learn...ty for helping me

Answer 18

That's the slope of the line or the rate of decrease of the relationship between the height of the glacier and the amount of years elapsed.

Answer 19

Well, I guess I was close to the correct answer, but as we know close is incorrect

Answer 20

Maybe I should have written it like this:

\[m = \frac{\Delta\text{Glacier Height}}{\Delta \text{Years}} \]

Answer 21

So, the yearly rate of change is; -3/85 Acres/year? Am I writing this correctly?

Answer 22

A negative fraction?

Answer 23

Yes, that is correct.

Answer 24

Negative because the glacier height is decreasing over time.

Answer 25

starting to smile...

Answer 26

We still need to figure out the linear equation though. The equation of a line is:\[ y = mx + b\]

Answer 27

Ok, so for the 2nd part...what is the linear equation that gives the acreage of the glacier t years after 1915?

Answer 28

The way that this is worded is so hard to understand

Answer 29

y=mx+b...is mx = the glacier height?

Answer 30

Not to worry, it just means that \(t\) is the variable we use for years rather than \(x\).

Answer 31

\(y\) is the glacier height
\(m\) is the slope of the line or rate of change between y and x
\(x\) is the amount of years that goes by

Answer 32

But in this case, \(x = t\)

Answer 33

Let's input the slope and one of our points to find b:

\[(2000) = -(3/85)(1) + b\]
\[2000 = -3/85 + b\]

Answer 34

Now we just need to solve for b

Answer 35

y is the glacier height?
t is the years?

Answer 36

oh no, have u left me??

Answer 37

I haven't left you.

Answer 38

Solve for b, then we can continue.

Answer 39

TY so much..LOL

Answer 40

is b = 86

Answer 41

(3/85)(1)+b = 86???

Answer 42

What's 2000 + 3/85 ?

Answer 43

I am unsure....I feel so dumb..

Answer 44

2385???

Answer 45

No

Answer 46

2000 with a fraction of 3/85??

Answer 47

Yes

Answer 48

Anytime you see something like that, you can re-write it as a mixed fraction:

\[2000\frac{3}{85}\]

Answer 49

b = 2000 3/85??

Answer 50

But we usually don't write b in that form

Answer 51

ok, I am listening

Answer 52

When we are done will also explain the hero/medal/fan process 2 me

Answer 53

Well, basically, what you do is sort of round off. 3/85 is closer to zero.

So \(b \approx 2000\)

Answer 54

so b is rounded off to the closest 0. b = 2000:)

Answer 55

A=3t/85 + 2000? This is the linear equation that gives the acreage of the glacier t years after 1915?

Answer 56

u there??

Answer 57

But wait...that slope should be negative.

Answer 58

\[A = 2000 - \frac{3}{85}t\]

Answer 59

So, that is my answer...A=2000-3/85 t ??? this is the linear equation that I am looking for?

Answer 60

Yes

Answer 61

The yearly rate of change is -3/85 & we are using t instead of x in the given formula

Answer 62

Ok, 1 last thing how do I commend u...MY HERO

Answer 63

I am new to this new friend!!

Answer 64

can i log in again & ask additional questions?

Answer 65

You can ask as many questions as you like.

Answer 66

how do I commend u & recognize u for your WONDERFUL EFFORTS

Answer 67

That's not really necessary.

Answer 68

ok, I REALLY APPRECIATE YOUR TIME & EFFORTS....MAYBE I could mail u a ham or something nice??? lol

Answer 69

Mail me a ham? That would be rather odd. I don't usually receive hams in the mail

Answer 70

Let me check something real quick.

Answer 71

LOL I have never mailed a ham.....TY

Answer 72

Okay, yep, the result has been confirmed correct.