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Thepotemich [5.8K]
2 years ago
6

Need answers ASAP 15 points!

Mathematics
1 answer:
VLD [36.1K]2 years ago
7 0

Answer:

Step-by-step explanation:

Part A: 5/26

Part B: 5/26+ 1/2 which is 18/26 or 9/13

Part C: 5/26 +21/25. 'without replacing' means there is one less option in the bag. So denominator becomes 26-1=25. Numerator is 21 because there are a total of 21 consonants in the alphabet. Since we removed a vowel and not a consonant, it will remain 21.

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Answer:

\frac{dP}{dt} = rP(1 - \frac{P}{K}) = 0.017P(1 - \frac{P}{16})

Step-by-step explanation:

The logistic function of population growth, that is, the solution of the differential equation is as follows:

P(t) = \frac{KP_{0}e^{rt}}{K + P_{0}(e^{rt} - 1)}

We use this equation to find the value of r.

In this problem, we have that:

K = 16, P_{0} = 2, P(50) = 4

So we find the value of r.

P(t) = \frac{KP_{0}e^{rt}}{K + P_{0}(e^{rt} - 1)}

4 = \frac{16*2e^{50r}}{16 + 2*(e^{50r} - 1)}

4 = \frac{32e^{50r}}{14 + 2e^{50r}}

56 + 8e^{50r} = 32e^{50r}}

24e^{50r} = 56

e^{50r} = 2.33

Applying ln to both sides of the equality

50r = 0.8459

r = 0.017

So

The differential equation is

\frac{dP}{dt} = rP(1 - \frac{P}{K}) = 0.017P(1 - \frac{P}{16})

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3 years ago
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