1. KATHERINE LORENA SILVA ALONSOCODIGO: 2073612METODOS NUMERICOS-534035-455295 <br />EJERCICIO PROPUESTO DE MODELO MATEMATICO<br />POPULATION GROWTH AND DECAY TIME<br />The population increased at a rate that is proportional to the number of people present at time t. if an initial population has doubled in five years.¿How many the populations take to triple and quadruple?<br />SOLUTION<br />Let P = p (t) the population at time t<br />Now solve the initial value problem, PVI<br />dPdt=kP , P0=P0<br />Pt=Cekt<br />Applying the initial condition<br />P0=P0e0=C<br />Pt=P0ekt<br />Is P5=2P0<br /> P5=2P0=P0=ek5<br />ln2=lnek5=5k<br />k=ln25=0.138<br />Pt=P0e0.138<br />Is P(t1)=3P0=P0e0.138t<br />t1 is the time that spend the population in be the triple <br />ln3=0.138t1<br />t1=ln30.138=8.4 years<br />Is Pt2=4P0<br />t2 is the time that spend the population in be the Quad<br />P(t2)=4P0=P0e0.183t<br />ln4=0.13t<br />t=ln40.13=10.66 years<br />
