Be sure you are acquainted with the two forms of the equations for exponential growth and decay. Recall that they are:
When introducing the equations, we mentioned a case of wee beasties. There were 10% increases in the population. One population began with a population of 100, and after a year, there were 110. The other population had a population of 5000, and one year later, it grew to 5500. Note the ratios of final to initial populations, 'N/', were both the same:
You can solve for 'k', the growth constant, for this particular example using the second equation. Since N/ = 1.1, and t = 1.0 (year), we have
Recall that an exponent must be dimensionless. So 'k' will always have dimensions of reciprocal time. In the case of the wee beasties, k has units of year.
Now that we know the value of the growth constant for our wee beasties, k = 0.0953, we can substitute this into our first equation.