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Current Question (ID: 13215)

Question:

The formula for exponential population growth is:-

Options:

1. dt/dN = rN
2. dN/rN = dt
3. rN/dN = dt
4. dN/dt = rN

Solution:

In J-shaped form of population growth, the density increases in an exponential manner and then a crash occurs or the increase stops abruptly as environmental resistance becomes effective. This is mathematically described by an equation of exponential or geometric increase, which is as follows: dN/dt = rN where, d = rate of change t = time N = number of females at a particular time r = biotic potential of each female (N can also be considered as the total population and r as the biotic potential of each individual). Fig.13.6. page 230, XII NCERT

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}