<em>Answer:</em>
<em>Final answer is approx 6.644 years.</em>
<em>Step-by-step explanation:</em>
<em>Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.
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<em>So we can use growth formula:</em>
<em>A = P (1 + r)^t</em>
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<em>Then we get equation for motorcycles and cars as:</em>
<em>A = 5.75 (1 + 0.16)^t</em>
<em>A = 3.5 (1 + 0.25)^t</em>
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<em>Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:</em>
<em>3.5 (1 + 0.25)^t > 5.75 (1 + 0.16)^t</em>
<em>3.5 (1.25)^t > 5.75 (1.16)^t</em>
<em>3.5 (1.25)t . 5.75 (1.16)^t</em>
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<em>(1.25)^t/(1.16) > 5.75/3.5</em>
<em>(1.25/1.16)^t > 1.64287514286</em>
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<em>t·In (1.25/1.16) > In (1.64287514286)</em>
<em>t > In(1.64285714286)/In (1.25/1.16)</em>
<em>t > 6.6436473051</em>
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<em>Hence final answer is approx 6.644 years.</em>