<Dl> <Dd> T d = (t 2 − t 1) ⋅ log ⁡ (2) log ⁡ (q 2 q 1). (\ displaystyle T_ (d) = (t_ (2) - t_ (1)) \ cdot (\ frac (\ log (2)) (\ log ((\ frac (q_ (2)) (q_ (1)))))).) </Dd> </Dl> <Dd> T d = (t 2 − t 1) ⋅ log ⁡ (2) log ⁡ (q 2 q 1). (\ displaystyle T_ (d) = (t_ (2) - t_ (1)) \ cdot (\ frac (\ log (2)) (\ log ((\ frac (q_ (2)) (q_ (1)))))).) </Dd> <P> A constant relative growth rate means simply that the increase per unit time is proportional to the current quantity, i.e. the addition rate per unit amount is constant . It naturally occurs when the existing material generates or is the main determinant of new material . For example, population growth in virgin territory, or fractional - reserve banking creating inflation . With unvarying growth the doubling calculation may be applied for many doubling periods or generations . </P> <P> In practice eventually other constraints become important, exponential growth stops and the doubling time changes or becomes inapplicable . Limited food supply or other resources at high population densities will reduce growth, or needing a wheel - barrow full of notes to buy a loaf of bread will reduce the acceptance of paper money . While using doubling times is convenient and simple, we should not apply the idea without considering factors which may affect future growth . In the 1950s Canada's population growth rate was over 3% per year, so extrapolating the current growth rate of 0.9% for many decades (implied by the doubling time) is unjustified unless we have examined the underlying causes of the growth and determined they will not be changing significantly over that period . </P>

6. how long would it take for a population with a 1.4 growth rate to double