1. The population P of a bacteria culture is modeled by =4100e", where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Rour che nearest tenth of an hour.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Problem Statement:**

1. The population \( P \) of a bacteria culture is modeled by the equation \( P = 4100e^{kt} \), where \( t \) is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour.

**Explanation:**

- The given model \( P = 4100e^{kt} \) is an exponential growth formula, where \( P \) is the population at time \( t \), 4100 is the initial population, \( e \) is the base of the natural logarithm, and \( k \) is the growth rate constant.
- The problem provides that after 40 hours, the population reached 5800.
- The task is to determine the time it will take for the population to double from its initial size using the provided model, and to present this time rounded to the nearest tenth of an hour.
Transcribed Image Text:**Problem Statement:** 1. The population \( P \) of a bacteria culture is modeled by the equation \( P = 4100e^{kt} \), where \( t \) is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour. **Explanation:** - The given model \( P = 4100e^{kt} \) is an exponential growth formula, where \( P \) is the population at time \( t \), 4100 is the initial population, \( e \) is the base of the natural logarithm, and \( k \) is the growth rate constant. - The problem provides that after 40 hours, the population reached 5800. - The task is to determine the time it will take for the population to double from its initial size using the provided model, and to present this time rounded to the nearest tenth of an hour.
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