What doubling time means

Doubling time is the number of equal periods needed for a repeating growth factor to reach exactly two times the starting amount. For discrete growth, the model solves (1+r)^t = 2.

Why the logarithm appears

Taking logarithms isolates the exponent, giving t = \ln 2 / \ln(1+r). Faster growth rates make the denominator larger, so the doubling time gets shorter.

Typical applications

This is useful in finance, business growth, technology adoption, and population modeling whenever people care more about “time to double” than about the value at a specific date.