Answer:
4.75 years are required to triple the population
Step-by-step explanation:
As we know
[tex]\frac{dP}{dt} = P\\[/tex]
Integrating both the side with respect to t we get
[tex]ln P = kt + c_1\\P = e^{kt + c_1}\\P = Ce^{kt}[/tex]
At t = 0, P = P0
[tex]2 P_0 = P_0 * e ^{3k}\\2 = e ^{3k}\\ln 2 = 3k\\k = 0.231\\[/tex]
substituting K value in main equation, we get -
[tex]P = P_0 * e^{0.231 * t}\\3P_0 = P_0 * e^{0.231 * t}\\3 = e^{0.231 * t}\\ln 3 = 0.231 * t\\t = 4.75[/tex]
4.75 years are required to triple the population
