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# Rate change

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.

### Comments

looks like the equation should be:  y = -0.043x + 5

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### 1 Answer

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

### Comments

I'm confused... y=0.043x+5 makes it look like the glacial acreage grows every year, but in fact the glacier is shrinking...

I'm sorry.  You are right.

The slope is -0.043 since the change is -4 acres/92 years.