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anonymous
 5 years ago
From 1953 to 1966 the number of automobiles in the country increased at an annual rate of 6.7 percent. What is the doubling time for growth in automobiles in the US?
anonymous
 5 years ago
From 1953 to 1966 the number of automobiles in the country increased at an annual rate of 6.7 percent. What is the doubling time for growth in automobiles in the US?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Annual increase is 6.7% . If initially N automobiles were there in 1953 After 1 year the no. of automobiles is (106.7/100)*N. After 2 years i.e, in 1955 it'll be (1.067)*(1.067)*N Similarly after x years it'll be $$(1.067)^{x} \times N$$ Make it equal to 2N since we need to find the time taken to double. $$(1.067)^x=2 \implies x=\frac{\ln2}{\ln1.067}=10.7$$ It takes ~11 yrs for the doubling of the automobiles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or: \[1.067^{x}=2 => x =\log_{1.067} 2\approx10.7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thankyou to both of you!
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