Due to erosion, the height of Math Mountain decreases at a rate of 2% every century.

If the the mountain was 18,000 ft in 2005, how tall was the mountain in 1505?

Question

Due to erosion, the height of Math Mountain decreases at a rate of 2% every century. 

If the the mountain was 18,000 ft in 2005, how tall was the mountain in 1505?

anonymous · Answer

we can model this as $18,000\times (.98)^t$ where $t$ is time in centuries

anonymous · Answer

that is because reducing a number by 2% is the same as multiplying it by $.98$

anonymous · Answer

since 1505 is 5 centuries BEFORE 2005, replace $t$ by $-5$ and see what you get

anonymous · Answer

i get 19,913 rounded http://www.wolframalpha.com/input/?i=18000%28.98%29^-5