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Example: Evaluating Exponential Growth
Suppose a researcher starts an experiment with an initial population of viruses () that grows continuously at a rate of per hour (). To determine the number of viruses after hours (), we use the exponential growth formula: . Substituting the given values into the equation yields , which simplifies to . Evaluating this expression gives an amount of approximately 40{,}342.88. Rounding to the nearest whole number, the researcher will find 40{,}343 viruses. This same procedural framework can be used to model other continuous biological growth scenarios, such as bacterial populations increasing over time.
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Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
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Example: Evaluating Exponential Growth
Try It 10.33: Evaluating Exponential Growth
Try It 10.34: Evaluating Exponential Growth
Example 10.44: Solving an Exponential Growth Application
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A city planner is evaluating the continuous growth of the local population using the formula . The current population is 50,000 and it is growing at a continuous rate of 2% per year. Which of the following shows the correct first step for evaluating the population after 10 years?
A laboratory researcher is using the continuous growth formula to model the expansion of a bacterial colony. Match each variable from the formula with the corresponding component of the researcher's growth model.
A laboratory researcher is using the continuous growth formula to predict the size of a bacterial population. Arrange the steps below in the correct procedural order to evaluate the final population based on the given experimental data.
A laboratory researcher uses the continuous growth formula to track a virus culture. In this formula, the variable represents the initial number of viruses present at the beginning of the study.
A quality assurance technician at a food processing plant is evaluating the continuous growth of a bacterial sample using the formula . If the sample grows continuously at a rate of 14% per hour, the decimal value that must be substituted for the variable is ____.
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