How long would it take for a colony of 20
cells to increase to a population of 1 million?

Question

How long would it take for a colony of 20
 ﻿cells to increase to a population of 1 ﻿million?

Accepted Answer

∻Answer∻ ⚹ It would take approximately 15.5 generations for a colony of 20 cells to increase to a population of 1 million cells. ⚹ ∻Solution∻ ‖ a ⋮ Determine the initial population size ($N_0$) and the final population size ($N$). Here, $N_0 = 20$ cells and $N = 1,000,000$ cells. ‖‖ b ⋮ Use the formula for exponential growth: $N = N_0 \cdot 2^n$, where $n$ is the number of generations. ‖‖ c ⋮ Rearrange the formula to solve for $n$: $n = \frac{\log(N / N_0)}{\log(2)}$. ‖‖ d ⋮ Substitute the given values into the formula: $n = \frac{\log(1,000,000 / 20)}{\log(2)}$. ‖‖ e ⋮ Calculate the value: $n = \frac{\log(50,000)}{\log(2)} \approx 15.5$. ‖ ∻Key Concept∻ ⚹ Exponential growth ⚹ ∻Explanation∻ ⚹ Exponential growth occurs when the growth rate of a population is proportional to its current size, leading to the population doubling at regular intervals. In this case, the number of generations required for the population to grow from 20 cells to 1 million cells can be calculated using the exponential growth formula. ⚹◊How does the growth rate of a cell population relate to factors such as nutrient availability and competition for resources?⍭ Generate me a similar question◊

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