which of the following expresses the change in the number of cells
LectureNotes said which of the following expresses the change in the number of cells?
Answer:
In mathematics and biology, the change in the number of cells is typically expressed by the derivative of the cell population size with respect to time. In symbols, if N(t) is the number of cells at time t, the rate of change of these cells is:
\frac{dN}{dt}
This notation explicitly represents how quickly the cell count is increasing or decreasing over time. Depending on the biological context, there are different models for this rate of change. Two common models are:
-
Exponential Growth Model
- Assumes unlimited resources (e.g., nutrient availability) and no constraints.
- Expressed as \displaystyle \frac{dN}{dt} = rN, where r is the growth rate.
-
Logistic Growth Model
- Recognizes a carrying capacity K, which is the maximum population the environment can support.
- Expressed as \displaystyle \frac{dN}{dt} = rN\Bigl(1 - \frac{N}{K}\Bigr), where r is the intrinsic growth rate.
Below is a table summarizing these key expressions that represent the rate of change (i.e., how N(t) evolves over time):
| Growth Model | Mathematical Expression | Key Characteristics |
|---|---|---|
| Exponential Growth | \displaystyle \frac{dN}{dt} = rN | • No upper limit on population • Growth rate proportional to N |
| Logistic Growth | \displaystyle \frac{dN}{dt} = rN\bigl(1 - \frac{N}{K}\bigr) | • Carrying capacity K • Growth rate decreases as N approaches K |
Keep in mind that in many real-world biological settings, logistic growth is more realistic than exponential growth, especially when resource limitations and population density factors (e.g., competition) are considered.
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