We could fit such model as in example 3.3 via Nonlinear Least Squares or we could try to linearize the relationship by a ln-transform of both DAY and LEAD:

Now we can us lm() to estimate the coefficients and check our model:

The residuals show no pattern:

From the model-output:

We see that out fitted model hast the formula:
with an R-squared of 0.77 and is statistically significant. The standard errors for the two parameters are 0.064 and 0.031.

So our backtransformed model would be:

Finally we can also plot our model:

Code and data are available at my github-repo under filename ‘p94’.