Taking the natural log of both sides:

Take the natural log of both sides:

Therefore, the mean lifetime is equal to the half-life divided by the natural log of 2, or:

The number 70 comes from the observation that the natural log of 2 is approximately 0.7, by multiplying this by 100 we obtain 70.

To find the doubling time we divide the natural log of 2 by the growth rate.

To find the time it takes to increase by a factor of 3 we would use the natural log of 3, approximately 1.1.

The intuition for transforming using the logit function (the natural log of the odds) was explained above.

First, take the natural log of both sides.

The parameter measures the increase in the natural log of the wage attributable to one more year of education.

The output voltage is expressed as the natural log of the input voltage.