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%.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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%.       Log On


   



Question 1206904: 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?

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Answer by ikleyn(52798) About Me  (Show Source):
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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?
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For the Canada population, the formula is

    C(t) = 30%2A1.014%5Et,  in millions.


For the Gremany population, the formula is

    G(t) = 80%2A0.983%5Et,  in millions.


t is the time in years from now.


The populatins are equal when  V(t) = G(t),  or

    30%2A1.014%5Et = 80%2A0.983%5Et.


It implies

    30%2F80 = %280.983%2F1.014%29%5Et,

or

    0.375 = 0.969428008%5Et.


Take log base 10 of both sides

    log(0.375) = t*log(0.969428008),

    t = log%28%280.375%29%29%2Flog%28%280.969428008%29%29 = use your calculator = 31.58965618


Round to the closest integer to get the 

ANSWER.  Approximately in 32 years.

Solved.

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