SOLUTION: The population of Canada is 30 million people and is growing at an annual rate of 1.4%. The population of Germany is 80 million people and is decreasing at an annual rate of 1.7%.

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Question 23218: The population of Canada is 30 million people and is growing at an annual rate of 1.4%.
The population of Germany is 80 million people and is decreasing at an annual rate of 1.7%.
In how many years will the population of Canada be equal to the population of Germany?
(Use logarithms to solve the resulting equation and answer accurate to 2 decimal places.)
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
WHAT A NEAT PROBLEM!! NICE!!

For Canada y=30+e%5E%28.014t%29+ in millions
For Germany y+=+80+e%5E%28-.017t%29+ in millions

When will populations be equal?
30+e%5E%28.014t%29+=++80+e%5E%28-.017t%29+

Divide both sides by 30+e%5E%28.014t%29:
%2830+e%5E%28.014t%29%29%2F%2830e%5E%28.014t%29%29++=++%2880+e%5E%28-.017t%29%29%2F%2830e%5E%28.014t%29%29+
+1++=++%2880+e%5E%28-.017t%29%29%2F%28+30e%5E%28.014t%29%29+

When you divide with the same base number, you subtract exponents:
1++=+%288%2F3%29++e%5E%28-.017t-+.014t%29+=+%288%2F3%29%2Ae%5E%28-.031t%29+

Multiply both sides by 3%2F8
3%2F8+=+e%5E%28-.031t%29
Take the ln of each side:
ln%283%2F8%29+=+ln%28e%5E%28-.031t%29%29+
ln+%283%2F8%29+=+-.031t
+t=+%28ln%283%2F8%29%29%2F+-.031
t=+31.639655 calculator accuracy
Rounds off to 31.64 years.

R^2 at SCC