For week 2, we mostly focused on geometric series, geometric sequences and infinite geometric series. I struggled more with these concepts than I did with arithmetic series and sequences.
Working through the geometric sequences assignment, I came upon a word problem that confused me. In general I struggle with math word problems so it didn’t surprise me that I would be confused with this one.
Ex : #14, pg 41 : Between the Canadian censuses in 2001 and 2006, the number of people who could converse in Cree had increase by 7%. In 2006, 87 285 people could converse in Cree. Assume the 5-year increase continues to be 7%. Estimate to the nearest hundred how many people will be able to converse in Cree in 2031.
I was very sure I could solve this question, but then I saw that the common ratio would be 7%. I knew I couldn’t just use 7 as the difference because that wouldn’t have made sense with the question. In the red text above, it says that the 5-year increase continues to be 7%. I had to refresh my memory about percentages by asking for help.
What I learned/refreshed my memory on was that the common ration couldn’t be 7 because that would just be multiplying something by 7. I also knew that my common ration couldn’t be 0.7 because that would’ve been a decrease. I came to the conclusion that my common ratio must be 1.07. The reason is because since 1 = the same amount, then I would have to add the 0.7 which = 1.07.
1.07 = increase
0.93 = decrease
There were a couple of questions in the book that talked about percentage and a question in our skills check that talked about percentages too. I think it was very useful refreshing my memory on this because this concept might come back in later sections of precalc11.