logistic groth model and USA population

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logistic growth mode $$P(t)=\frac{P_l}{1-ce^{-k*t}} $$

$P_l$,$c,k$ are constants P(t) population at time t $P_L$ is the carrying capacity

find constants with $P(0)=76.212$,$P(30)=122.775$,$P(60)=179.323$


$t=0$

$$P(0)=\frac{P_l}{1-c}=76.212 $$

$t=30$

$$P(30)= \frac{76.212 *(1-c) }{1-ce^{-k*30}}=122.775$$

$t=60$

$$P(60)= \frac{76.212 *(1-c) }{1-ce^{-k*60}}=179.323$$

can use newtons method and matlab if can see how put in form $f(x)$ and find the roots. Tryied to tell sage and wolframm alpha to solve for constants but having issues