Question

Solve this one too, please! Thx

Answer 1

P(100) ≈ 6.977 million

Explanation:

The question asks for the population of New York state in the year 1900, based on the given mathematical model, P(t). To find this, we will substitute t = 1900 − 1800 = 100 into the formula and calculate the value of P(t), rounding it to the nearest thousandth.

Given:

`P(t) = (19.71)/(1 + 61.22e^(-0.03513t))`

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Substitute t = 100 into the formula:

`\Longrightarrow P(t) = (19.71)/(1 + 61.22e^(-0.03513t))\\\\\\\\\Longrightarrow P(100) = (19.71)/(1 + 61.22e^(-0.03513(100)))`

Evaluating this using a calculator, we get:

`\Longrightarrow P(100) = 6.97747\\\\\\\\\therefore \boxed{\boxed{P(100) \approx 6.977 \ \text{million}}}`

Therefore, the population of New York state in the year 1900 was approximately 6.977 million, rounded to the nearest thousandth.