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Try It 10.34: Evaluating Exponential Growth
Suppose a biologist 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 . Therefore, the biologist will find viruses.
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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
Half-Life
A marketing manager uses the exponential growth and decay formula to forecast the number of subscribers for a new digital service. Match each variable from the formula with the specific role it plays in this business projection.
A logistics manager uses the formula to model the depreciation (loss of value) of a delivery truck over several years. To correctly show that the truck's value is decaying, which condition must be met by the constant ?
A laboratory supervisor uses the formula to model the decay of a chemical sample over time. In this formula, the variable represents the ____ amount of the chemical present at the beginning of the observation.
A facilities manager uses the formula to model the decay of a backup power supply's charge over time. True or False: This formula is used to model decay that occurs in fixed daily intervals rather than at a continuous rate.
Differentiating Growth and Decay in Professional Modeling
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A biologist starts an experiment with an initial population of viruses that grows continuously at a rate of per hour. Using the formula , which of the following is the approximate population of viruses after hours?
In a clinical research study, a lab technician monitors a viral culture that starts with 100 viruses and grows continuously at a rate of 10% per hour for 24 hours. Using the exponential growth formula , match each variable to its specific role or value within this research scenario.
A laboratory technician at a biotechnology company is modeling the continuous growth of a viral culture. The culture starts with 100 viruses and grows at a continuous rate of 10% per hour. To calculate the population after 24 hours using the formula , the technician simplifies the expression to . The numerical value of the exponent is ____.
A laboratory researcher uses the formula to model the continuous growth of a viral population. In this mathematical model, the variable represents the initial number of viruses present at the start of the study.
As a data analyst training a new laboratory assistant, you need to outline the standard procedural steps for modeling continuous viral growth. Arrange the following steps in the correct chronological order to determine the final population of a culture that starts with 100 viruses and grows continuously at a rate of 10% per hour over a 24-hour period.