During the 1980s, U.S. car and truck miles traveled increased by 4% per year, bu

To calculate doubling time (in years):
\({{T}_{d}} = \frac{log (2)}{log \frac{{{X}_{f}}}{{{X}_{i}}}}\)

For the miles traveled:
Since miles increase per year, we add the 4% (0.04) to the original 100%:
Xf = 1.04Xi:
\({{T}_{d}} = \frac{log (2)}{log \frac{1.04{{X}_{i}}}{{{X}_{i}}}}\)

Cancel Xi from top and bottom:
\({{T}_{d}} = \frac{log (2)}{log (1.04)}\)

Now, plug into a calculator:
Td = 17.672987 years

For the highway miles:
Use the doubling time formula again:

This time, the increase is only 0.1%, or 0.001.  Therefore, Xf = 1.001Xi:
\({{T}_{d}} = \frac{log (2)}{log \frac{1.001{{X}_{i}}}{{{X}_{i}}}}\)

Cancel Xi from top and bottom:
\({{T}_{d}} = \frac{log (2)}{log (1.001)}\)

Now, plug into a calculator:
Td = 693.493 years

thank you for your help