SOLUTION: can you help me with this problem China is one of the biggest potential markets for US autos. In 2010, there were 1.38E8 car owners in China and the number was growing with a doub

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: can you help me with this problem China is one of the biggest potential markets for US autos. In 2010, there were 1.38E8 car owners in China and the number was growing with a doub      Log On


   



Question 767982: can you help me with this problem
China is one of the biggest potential markets for US autos. In 2010, there were 1.38E8 car owners in China and the number was growing with a doubling time of 6.3 years. How many car owners would you predict for that country in 2020? Owners (E notation, 2 decimals)??

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For now, say there are +n+ car owners in China in 2010
Also, for now, say the number doubles every +t+ years
Let +C+ = current number of car owners
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After +t+ years, there are:
+C+=+n%2A2%5E1+
After +2t+ years, there are
+C+=+n%2A2%5E2+
After +3t+ years, there are
+C+=+n%2A2%5E3+
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So, the general formula would be
+C+=+n%2A2%5Ek+ where k*t is the years
since 2010
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From 2010 to 2020 is +10+ years, so
+k%2At+=+10+
+t+=+6.3+
+k%2A6.3+=+10+
+k+=+1.5873015+
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In 2020, there will be:
+C+=+1.38%2A10%5E8%2A2%5E1.5873+
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I can't find my calculator, but you need to convert
+2%5E1.5873+ to a number that looks like a.aaa x 10^n
Then multiply by +1.38%2A10%5E8+
Then get it back to looking like a.aaa x 10^n