Question

A scientist is growing cells in a petri dish. Which of the following equations could model the number of cells in the petri dish after x days?(1 point) Responses y=(14)x y equals left parenthesis Start Fraction 1 over 4 End Fraction right parenthesis superscript x baseline y=15(0.99)x y equals 15 left parenthesis 0.99 right parenthesis superscript x baseline y=10(2)x y equals 10 left parenthesis 2 right parenthesis superscript x baseline y=100(0.2)x

Answer 1

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:

1. **\(y = (14)^x\)**:
- 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.**

2. **\(y = \left( \frac{1}{4} \right)^x\)**:
- 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.**

3. **\(y = 15(0.99)^x\)**:
- 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.**

4. **\(y = 10(2)^x\)**:
- This represents exponential growth, where the number of cells doubles every day. This is a common model for cell division and biological growth. **Suitable.**

5. **\(y = 100(0.2)^x\)**:
- 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:

**\(y = 10(2)^x\)**.