Answer:
the initial population was 155027 people
Step-by-step explanation:
since the rate of increase of the population is proportional to the population itself, then the corresponding formula for a population P and time t is
dP/dt = k*P , where k= constant
dP/P = k*dt
∫dP/P =∫ k*dt
integrating between time t=0 (with P=Pâ‚€) and time t=t (with P=P)
ln (P/Pâ‚€)=k*t
if the population was P= 171000, at t=4 years then
ln (171000/Pâ‚€)=k* 4years
then the population is P=247000 att=19 years , thus
ln (247000/Pâ‚€)=k*19 years
diving both equations
ln (247000/Pâ‚€) / ln (171000/Pâ‚€) =19 years/ 4 years
ln (247000/Pâ‚€) = ln (171000/Pâ‚€)^(19/4)
Pâ‚€/247000 = (Pâ‚€/ 171000)^(19/4)
(171000)^(19/4) / 247000 = (Pâ‚€)^(19/4) / Pâ‚€ = Pâ‚€^(15/4)
Pâ‚€ = 171000^(19/15) /[247000^(4/15) ] = 155027 people
therefore the initial population was 155027 people
