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zimovet [89]
3 years ago
14

The instructions are:

Mathematics
1 answer:
Darina [25.2K]3 years ago
5 0
Comment if you need clarification!

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For the parallelogram find the value of x,y,and z
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Step-by-step explanation:

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The rate of change (dP/dt), of the number of people on an ocean beach is modeled by a logistic differential equation. The maximu
Kazeer [188]

Answer:

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Step-by-step explanation:

The logistic differential equation is as follows:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

In this problem, we have that:

K = 1200, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that \frac{dP}{dt} = 400 when P = 200. With this, we can find r, that is, the growth rate,

So

\frac{dP}{dt} = rP(1 - \frac{P}{K})

400 = 200r(1 - \frac{200}{1200})

166.67r = 400

r = 2.4

So the differential equation is:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

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