Amma studies bacteria growth in a lab. She has observed a rise in the bacteria count over ten hours. Each hour there are 5% more bacteria. Amma would like to predict the count of bacteria in 6 hours from now.Which type of trendline would be the best choice to model the relationship between hours and bacteria count?Group of answer choicesExponentialThere will not be a predictable relationship between the two variables.QuadraticLinear
Question
Amma studies bacteria growth in a lab. She has observed a rise in the bacteria count over ten hours. Each hour there are 5% more bacteria. Amma would like to predict the count of bacteria in 6 hours from now.Which type of trendline would be the best choice to model the relationship between hours and bacteria count?Group of answer choicesExponentialThere will not be a predictable relationship between the two variables.QuadraticLinear
Solution
To determine the best type of trendline to model the relationship between hours and bacteria count, we need to consider the nature of the growth described.
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Exponential Growth: This type of growth occurs when the rate of change of a quantity is proportional to the current quantity. In this case, the bacteria count increases by 5% each hour, which means the growth rate is proportional to the current count. This is a classic example of exponential growth.
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Linear Growth: This type of growth occurs when the quantity increases by a constant amount each time period. Since the bacteria count increases by a percentage (not a constant amount), linear growth is not appropriate here.
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Quadratic Growth: This type of growth occurs when the quantity increases by an amount that is proportional to the square of the time period. This is not applicable to the scenario described, as the bacteria count increases by a percentage each hour, not by a factor related to the square of the time.
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No Predictable Relationship: Given that the bacteria count increases by a consistent percentage each hour, there is a predictable relationship between the two variables.
Given the information, the best choice to model the relationship between hours and bacteria count is:
Exponential
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