Answer:

Explanation:
The population of New York state can be modeled by the function:

where:
- P is the population in millions
- t is the number of years since 1800.
The maximum sustainable population can be calculated by finding the limit of the population function P(t) as time (t) approaches infinity.
As t approaches infinity, the exponential term e^(-0.03513t) will approach zero. Therefore:

So, the limit of the population function as t approaches infinity is:

Therefore, the estimated maximum sustainable population of New York rounded to the nearest thousandth is:


Note: When asked to round an answer to the nearest thousandth, we round to the third decimal place.