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Margaret [11]
2 years ago
8

2. A discrete population of Sword-billed Hummingbirds follows the logistic growth equation and is characterized by the following

parameters. Estimate the population one time step into the future.
r = 0.14
N0 = 690
K = 1060
Mathematics
1 answer:
hodyreva [135]2 years ago
4 0

The population one time step into the future is 33.71886792708

The logistic growth formula is:

\frac{dN}{dt} =r.N.\frac{(K-N)}{K}

where:

\frac{dN}{dt}=Logistic Growth

r = maximum per capita growth rate of population

N = population size

K =  carrying capacity

We have

r = 0.14

N0 = 690

K = 1060

<u>Substituting the values</u> in the <u>formula</u> ,we get

\frac{dN}{dt} =( 0.14).690.\frac{(1060-690)}{1060}\\=33.71886792708 per day

Therefore, the <em>population </em>one time step into the future is 33.71886792708.

Learn more:brainly.com/question/12881619

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Complete the table of values for the equation, 16x + 4y = 12.
Ann [662]

The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

<h3>Linear Function</h3>

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

  • a= the slope;
  • b=the constant term that represents the y-intercept.

The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x  for finding the values of y.

Thus,

  • For x= -2,  the value of y will be:

       16*(-2)+4y=12

      -32+4y=12

      4y=12+32

     4y=44

      y=11

  • For x= -1,  the value of y will be:

         16*(-1)+4y=12

  • -16+4y=12
  • 4y=12+16
  • 4y=28
  • y=7
  • For x= 0,  the value of y will be:

         16*(0)+4y=12

  • 0+4y=12
  • 4y=12
  • 4y=12
  • y=3
  • For x= 1,  the value of y will be:

         16*(1)+4y=12

  • 16+4y=12
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  • For x= 2,  the value of y will be:

         16*(2)+4y=12

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Read more about the linear equation here:

brainly.com/question/1884491

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Work out the volume of the shape​
pashok25 [27]

Answer:

\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}

Step-by-step explanation:

We have the cone and the half-sphere.

The formula of a volume of a cone:

V_c=\dfrac{1}{3}\pi r^2H

r - radius

H - height

We have r = 7cm and H = (22-7)cm=15cm. Substitute:

V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ cm^3

The formula of a volume of a sphere:

V_s=\dfrac{4}{3}\pi R^3

R - radius

Therefore the formula of a volume of a half-sphere:

V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3

We have R = 7cm. Substitute:

V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3

The volume of the given shape:

V=V_c+V_{hs}

Substitute:

V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3

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