Question

a certain mountain has elevation of 19,515 feet.in 1915, the glacier on this peak covered 6 acres.by 2002 this glacier had melted to only 1 acre.
(a) assume that this glacier melted at a constant rate each year.find this yearly rate.
(b) use your awser form part(a) to wite a linear equation that gives the acreage a of this glacier t years past 1915.
the yearly rate of change is__acres/year.
what is the equation that gives the acreage of the glacier t yaers after 1915?

Answer 1

im lost

Answer 2

use the points (0, 6) and (87, 1) to find the slope, or m, also the yearly rate of change. I got 87 because that is how many years elapsed from 1915 to 2002. If the equation has to be in standard form, use y=mx+b. You already will have solved for m, and then use the first x,y coordinate to determine b. This will give you the equation

Answer 3

(87/2,7/2)

Answer 4

are you thinking of the midpoint formula? Slope would be (y2-y1)/(x2-x1)

Answer 5

im lost

Answer 6

ok it 87 acres

Answer 7

a year

Answer 8

slope=m= (1-6)/ (87-0) = -5/87 acres/year which intuitively makes sense that its negative because the glacier size is decreasing. This was derived by finding the change in y (5 acres over that period of time) divided by the elapsed time (87 years)

Answer 9

5/87 acres/year

Answer 10

actually \(-\frac{5}{87}\) since they are decreasing

Answer 11

so if \(x\) is the number of years after 1915 then the equation would be
\[y=-\frac{5}{87}x+6\]

Answer 12

the reason for the \(6\) out at the end is because that is what you started with
i.e. if \(x=0\) then \(y=6\)