From 1953 to 1966 the number of automobiles in the country increased at an annual rate of 6.97 percent. What is the doubling time for growth in automobiles in the US?

Answer: about 10 years.

1) annual rate of growth = 6.97 % = > growth factor = (1 + 0.0697) ^n, where n is the number of years.

2) doubling time growth = > factor = 2

3) equation: 2 = (1 + 0.0697) ^n

4) solve the equation

- take logarithms: lg (2) = n * log (1+0.0697)

- divide both sides by log (1+0.0697) : n = log (2) / log (1.0697)

- result: n = 10.29

Conclusion: the double time is about 10 years.