But sometimes things can grow or the opposite. Xt x 0 1 r100 t is used when there is a quantity with an initial value x 0 that changes over time t with a constant rate of change r. 2A0 A0ekt 2 ekt Divide by A0 ln2 kt Take the natural logarithm t ln2 k Divide by the coefficient of t Thus the doubling time is.
So we have a generally useful formula.
In such cases I find it best to start plotting the graphs on the graph paper one by one. The general rule of thumb is that the exponential growth formula. If ft is an exponential function then the quantity is a constant sometimes called the time constant it is the reciprocal of the exponential growth constant or decay constant. Systems that exhibit exponential growth follow a model of the form.