Question
Consider a population of 10 million cells. Given the per-capita birth rate of 0.002 (per unit time) and the per-capita death rate of 0.002 (per unit time), the expected number of cells after 10 generations is
This question was previously asked in
NEET UG Re-Exam 2026 Question Paper (21-Jun-2026)
The correct answer is
10 million
Understanding Per-Capita Growth Rate
The per-capita growth rate ($r$) of a population is determined by subtracting the per-capita death rate ($d$) from the per-capita birth rate ($b$).
The formula is: $ r = b - d $ In this case:
- Per-capita birth rate ($b$) = 0.002
- Per-capita death rate ($d$) = 0.002
Calculating the per-capita growth rate:
$ r = 0.002 - 0.002 = 0 $A per-capita growth rate of 0 indicates that the population size remains constant because the number of births equals the number of deaths.
Population Calculation Over Generations
The expected number of cells after a certain number of generations ($n$) can be calculated using the formula for discrete population growth:
$ N_n = N_0 (1 + r)^n $Where:
- $N_n$ = Population size after $n$ generations
- $N_0$ = Initial population size
- $r$ = Per-capita growth rate per generation
- $n$ = Number of generations
Given:
- Initial population ($N_0$) = 10 million cells
- Number of generations ($n$) = 10
- Per-capita growth rate ($r$) = 0
Substitute the values into the formula:
$ N_{10} = 10,000,000 \times (1 + 0)^{10} $ $ N_{10} = 10,000,000 \times (1)^{10} $ $ N_{10} = 10,000,000 \times 1 $ $ N_{10} = 10,000,000 $Therefore, the expected number of cells after 10 generations is 10 million.
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