EXPONENTIAL GROWTH 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: As you can see, for a one year interval, this ratio was 1.1.

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

ln (1.1) = k (1.0)
Since ln (1.1) = 0.09531, then k = 0.0953/year. 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. Suppose the initial population were 2000 and we wish to calculate what it will be in 5.5 years. We know 'k' (= 0.0953 year ), 't' (= 5.5 year), and ' ' (= 2000). Then we can calculate 'N': Note that if the growth constant 'k' were larger, then 'kt' would be larger at any given time, and so the increase in population would be greater. Exponential Decay Return to: Exponential Growth and Decay Menu Exit to: Physics Tutorial Menu