Question

A certain mountain has elevation of 19,017 feet. In 1917 the glacier on this peak covered 6acres. By 2002 this glacier had melted 1 acre. Assume that the glacier melted at a constant rate each year. Find this rate

Answer 1

@dloada
By 2002, did the glacier cover 1 acre or did its cover decrease by 1 acre?

Answer 2

It decreased i believe

Answer 3

K. Then we have:

The rate of change is the slope of the secant of the two points on the graph of 'Time vs Area of Glacier coverage'. Where the x-axis is time and the y-axis is the area covered by the glacier. This gives us:

Rate of change = (5 - 6) / (2002 - 1917) = -1/85

Therefore, the glacier is melting at a rate of -1/85 acres/year

@dloada

Answer 4

What is the equation that gives the acreage of the glacier t years after 1917? A=

Answer 5

There is no equation. We aren't given one. We are only given 2 years, and 2 values of acres. We don't know the amount of area covered by the glacier in the years between 1917 and 2002. So when we draw the graph, we only know these 2 points. By simply graphing these two points on a graph and labelling x-axis as time in years and y-axis as area covered by glaciers, we notice that the point when x = 2002, has a y value of y = 5
And when x = 1917, y = 6.

Rate of change is always equal to change in y / change in x. Our change in y was -1 and y was 85. That gives us a rate of -1/85 acres/year at which the glacier is melting. The value is negative because the area covered by the glacier is decreasing.

@dloada

Answer 6

It's given that the glacier melted at a uniform rate. So we'll assume that each year it melted by the same area.
in 85 years it melted by 1 acre
Let the rate of melting( specifically average rate) be \(\frac{\Delta m }{\Delta y}\)
\(\Delta y= no.\ of\ years \)
so
\[\frac{\Delta m}{\Delta y}=\frac{1 acre}{85 years}=0.0117 acres/year\]