Given that during the period from 1790 to 1930, the US population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solution of the initial value problem.

$\frac{dP}{dt} =0.03135P =0.0001489P^2, P(0) = 3.9$

a) 1930 population is the population at time t = 40 years taking base year as 40

We can solve the differential equation using separation of variables

$\frac{dP}{0.03135P – 0.0001489P^2 } =dt\\\frac{dP}{-P(0.03135 – 0.0001489P } =dt$

Resolve into partial fractions

$\frac{31.8979}{P} -\frac{0.00474}{0.0001489P-0.03135}$

Integrate to get

ln P -0.00474/0.0001489 (ln (0.0001489P-0.03135) = t+C

ln P -31.833 (ln (0.0001489P-0.03135) =t+C

$\frac{P}{( ( (0.0001489P-0.03135)^{31.833} } =Ae^t$

Limiting population would be infinity.

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A is your answer because you would need divide 117 by 6 then add 6.95 to each appetizer to get 26.45.

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3 years ago

One equation in a system of equations with no solution is y=-20 +5.

Trava [24]

Answer:

the answerr is i9 dont know haha bum

Step-by-step explanation:

hahay

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2 years ago

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