A rancher is selling off 7% of her ranch each year. If she owns 2000 square miles, in
about how many years will she own only 600 square miles?

Question

A rancher is selling off 7% of her ranch each year. If she owns 2000 square miles, in
about how many years will she own only 600 square miles?

anonymous · Answer

If she starts with 100% of the land and sells 7%, she will have 93% of the land left. After n
years, she will have 2000(0.93)n of the land left. At least I think this is a start.

anonymous · Answer

Every time I try and do this problem I always get -0.49 which does not make any sense

anonymous · Answer

$$\left(\frac{93}{100}\right)^n=\frac{600}{2000} $$$$n=\frac{\log \left(\frac{10}{3}\right)}{\log \left(\frac{100}{93}\right)}=16.59 $$$$\left(\frac{93}{100}\right)^{16.59}=0.300008 $$