To model the growth of cells in a petri dish after x days, we need to consider whether the growth is exponential or not. Typically, cell growth can be exponential, meaning the number of cells increases by a constant rate proportional to the current number of cells.
Here's a breakdown of the provided equations to identify which one (or more) can be a suitable model:
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\(y = (14)^x\):
- This suggests that the number of cells grows based on powers of 14, which is not a common model for biological growth. This model grows extremely quickly and is unlikely to represent normal cell growth. Not suitable.
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\(y = \left( \frac{1}{4} \right)^x\):
- This indicates a decay model since the base is less than 1. This suggests cells decrease over time, which does not model growth. Not suitable.
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\(y = 15(0.99)^x\):
- Similar to the previous one, this has a base less than 1. This indicates a declining number of cells over time (99% of its value each day), which again does not model cell growth. Not suitable.
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\(y = 10(2)^x\):
- This represents exponential growth, where the number of cells doubles every day. This is a common model for cell division and biological growth. Suitable.
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\(y = 100(0.2)^x\):
- Like the previous decay models, this indicates a decrease (since \(0.2 < 1\)). This will yield a lower number of cells over time. Not suitable.
Based on this analysis, the only suitable model that captures the growth of cells in a petri dish after x days is:
\(y = 10(2)^x\).