The population of a country increases at a rate proportional to the number of inhabitants. If the population doubles in 30 years, find after how many years the population will triple–
Text Solution
Verified by ExpertsA
Let Population = x, time = t (in years)
Given 
∝ x ⇒ 
= kx
Where k is a constant of proportionality
or 
= k dt
Integrating, we get
l n x = kt + l n c
⇒ l n 
= kt ⇒ 
= e kt
or x = ce kt
If initially i.e., when time t = 0, x = x 0
then x 0 = ce 0 = c
∴ x = x 0 e kt
Given x = 2x 0 , t = 30
Then 2x 0 = x 0 e 30k ⇒ 2 = e 30k
∴ l n 2 = 30 k... (1)
To find t, when it triples, x = 3x 0
∴ 3x 0 = x 0 e kt ⇒ 3 = e kt ... (2)
Dividing (2) by (1) then 
= 
or t = 30 × 
= 30 × 1.5849 = 48 years
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