The intrinsic rate of increase(r), can be calculated by the following exponential growth equation:

N_t = N₀e^rt     ......(i)

Where, N_t = 2x

N₀ = x

t = 3

∴ From equation (i)

In N_t = In N₀ + lne^rt  (taking natural log)

= ln N₀ + rt lne

= lnN₀ + rt  (lne = 1)

or r = \(\frac{lnN_t -lnN_0}{t}\)

or r = \(\frac{lnN_t /N_0}{t}\)

or rt = 2.303 log \(\frac{2x}{x}\)

(∵ ln \(\frac{2x}{x}\) = 2.303 log₁₀ \(\frac{2x}{x}\))

or r = \(\frac{2.303 \times .301}{3}\) = \(\frac{0.6931}{3}\) = 0.231

or 23.1%