A population grows exponentially if sufficient amounts of food resources are

available to the individual. Its exponential growth can be calculated by the

following integral form of the exponential growth equation: 

Where,
N${}_t$ = Population density after time t
N${}_O$ = Population density at time zero
r = Intrinsic rate of natural increase
e = Base of natural logarithms
(2.71828)
From the above equation, we can calculate the intrinsic rate of increase (r) of a
population.
Now, as per the question,
Present population density = x
Then,
Population density after two years = 2x
t = 3 years
Substituting these values in the formula, we get:
⇒ 2x = x e${}^{3r}$
⇒ 2 = e${}^{3r}$
Applying log on both sides:
⇒ log 2 = 3r log e

$\Rightarrow 2x=x e^{3r}$
$\Rightarrow 2=e^{3r}$
$Applying \log on both sides:$
$\Rightarrow \log 2= 3r \log e$
$\Rightarrow \frac{\log 2}{3 \log e}=r$
$\Rightarrow \frac{\log 2}{3\times 0.434}=r$
$\Rightarrow \frac{0.301}{3\times 0.434}=r$
$\Rightarrow \frac{0.302}{1.302}=r$
$\Rightarrow 0.2311=r$