Rate of change between 9 acres in 1924 and 1 acre in 2002

Question

A certain mountain has an elevation of 19319 feet. In 1924 the glacier on it's peak covered 9 acres. By 2002 the glacier had melted to only 1 acre. What is the yearly rate of change

 

The yearly rate of change is how many acres per year?

 

What is the equation that gives the acreage of the glacier t years after 1924?

Answer 1

If the acreage decreases by the factor x (where 0<x<1) per year then in 1925 its acreage is 9x, in 1926 its acreage is 9x², and so on. 2002-1924=78 years, so 9x⁷⁸=1.

78log(x)+log(9)=0, 78log(x)=-log(9), log(x)=-log(9)/78=-0.01223 approx, x=0.9722=97.22%.

So the glacier decreases in acreage by 100-97.22=2.78% per year.