Respuesta :
It will take 13.9 years to double the population.
Here, dx/ dt ∝ x
and let x be the population at any time t
Then, dx/ dt = rx
where, r is proportionality constant.
Rewriting, dx/x= r dt
Integrating, ln x=rt + c
where, c is the integration constant
Exponentiating on both sides with e,
⇒x= ert + c
⇒ x= k ert
where, k = ec
Let x₀,
Here, r is the rate of increase, and k is the initial population
So, x = 2x₀,
Given to find the time t taken to attain double population,
So, x= k ert
⇒2x₀= x₀ e 0.05t ÷ x₀, we have 2 = e0.05t
Taking log on both sides, ln2 = ln(e0.05t)
⇒0.69314=0.05t
⇒t = 0.69317 = 40.05
⇒ t = 13.86294 years
Rounding up 13.86294 as 13.9
So, it takes 13.9 years to attain double population.
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