Question

The population of New York state can be modeled by:

Answer 1

Answer:

The answer is "19.71 million".

Step-by-step explanation:

$\to P(t) = \frac{19.71}{1+61.22 e^{(-0.03513t)}}$

where

$\to p= \text{population in million} \\\\\to t= \text{time in years}$

when t is increases, then $61.22 \ e^{-0.035 t}=\frac{61.22}{e^{0.035t}}$ when decrease so that p(t) continually grows in size to reach the optimum population which you find if t is quite high $t \to \infty$

$\to P_{max} = \lim_{ \ t \to \infty} \frac{19.71}{1+61.22 e^{(-0.03513t)}}$

$when \ t \to \infty \ , 0.035 t \to \infty \ , e^{(0.03513t)} \to e^{\infty} \to \infty\ \ e^{\frac{1}{0.035t} = \ e^{-0.035t}} \to 0$

           $= \frac{19.71}{1+0}\\\\= \frac{19.71}{1}\\\\ = 19.71 \ million$