A certain mountain has an elevation of 19,762 feet. In 1908, the glacier on this peak covered 5 acres. By 2000 this glacier had melted to only 1 acre. Assume that this glacier melted at a constant rate each year. Find the yearly rate.
I also need to find out how to write a linear equation that gives the acreage.
On Cartesian coordinate system, your X values (independent variable) will be years. Y values (dependent variable) will be acreage.
This is a span of 92 years (2000-1908), with a change in acreage of 4 acres (5 acres-1 acre).
4 acres/92 years=0.043 acres/yr
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A constant rate of melting implies a linear relationship.
A linear equation is y=mx+b, where m is your slope and b is the y-intercept.
This is a change over time, and is thus your slope. The y-intercept is your y-value at t0, or where you start your measurement (1908).
y=0.043x+5
I'm confused... y=0.043x+5 makes it look like the glacial acreage grows every year, but in fact the glacier is shrinking...
- Bill F. 1/13/2013I'm sorry. You are right.
The slope is -0.043 since the change is -4 acres/92 years.
- Ame R. 1/18/2013
WyzAnt.com
Comments
looks like the equation should be: y = -0.043x + 5
- Herb K. 1/17/2013