Question

Which of the following formula is correct to calculate "the average rate of change in the number of organisms per time, per organisms", in population growth rate ?
Where, N represent the number of organisms and t is the time.

• A. \(\Delta N\)
• B. \(\dfrac{\Delta N}{N \, \Delta t}\)
• C. \(\dfrac{\Delta N}{\Delta t}\)
• D. \(\dfrac{\Delta t}{N \, \Delta N}\)

Hint:

Per capita growth rate = change in number divided by (number of organisms times the time interval).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Population growth can be measured in two ways. One is the total rate, the number added per unit time. The other is the per capita rate, the number added per unit time for each individual already there.

Step 2: Method: build the expression by units:
Count the units. Change in number has the unit of organisms. Dividing by time gives organisms per time. Dividing again by the number of organisms gives 1 per time, which is the unit of a per capita rate.

Step 3: Write the expression:
Using this unit count, the rate is \[ \frac{\Delta N}{N \, \Delta t} \] and this is option 2.

Step 4: Reject the others:
Option 1 has the unit of organisms only. Option 3 has organisms per time, so it lacks the per organism division. Option 4 has time in the numerator, which gives units of time squared per organism squared, so it cannot be a growth rate.

Step 4b: Sample check with numbers:
Take a population of 200 organisms that adds 20 new organisms in 5 years. The total rate is 20 divided by 5, which is 4 organisms per year. The per organism rate is 20 divided by 200 times 5, which is 0.02 per organism per year. Only the formula in option 2 gives this second kind of value.

Final Answer:
Option 2 is correct. \[ \boxed{\frac{\Delta N}{N\,\Delta t}} \]