To model the growth of a population of cells in a petri dish over time, we typically look for a function that reflects either exponential growth or decay.
- Exponential growth is characterized by a base greater than 1 (e.g., \(y = ab^x\) where \(b > 1\)).
- Exponential decay is characterized by a base between 0 and 1 (e.g., \(y = ab^x\) where \(0 < b < 1\)).
Given the provided equations:
- \(y = 100(0.2)^x\): This represents exponential decay because the base \(0.2 < 1\).
- \(y = 14^x\): This represents exponential growth because \(14 > 1\).
- \(y = \left(\frac{1}{4}\right)^x\): This represents exponential decay because \(\frac{1}{4} < 1\).
- \(y = 15(0.99)^x\): This represents exponential decay because the base \(0.99 < 1\).
- \(y = 10(2)^x\): This represents exponential growth because \(2 > 1\).
Based on typical biological growth, the models that more commonly apply are those of exponential growth. Therefore, the equations representing exponential growth from the options provided are:
- \(y = 14^x\)
- \(y = 10(2)^x\)
However, if we consider models appropriate for cell growth that include a starting quantity, \(y = 10(2)^x\) and \(y = 14^x\) would be the choices leaning towards growth.
If we need to select one model that best represents cell growth in a petri dish, it would likely be:
\(y = 10(2)^x\), representing a scenario where the cells are doubling each day starting from a quantity of 10.
If you need only one answer, then choose \(y = 10(2)^x\) as a model representing cell growth after x days.
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