**Bacterial Growth of Streptococcus pneumoniae**The bacteria *Streptococcus pneumoniae* (*S. pneumoniae*) is the cause of many human diseases, the most common being pneumonia. A culture of these bacteria initially has 10 bacteria and increases at a rate of 25% per hour.---**Tasks:****(a) Calculate the Hourly Growth Factor:**Determine the growth factor per hour.\[ a = \_\_\_ \]**Exponential Model for Bacteria Count:**Develop an exponential model $ f(t) = Ca^t $ for the bacteria count in the sample, where $ t $ is measured in hours.\[ f(t) = \_\_\_ \]**(b) Predict Bacteria Count After 4 Hours:**Using the model found, estimate the number of bacteria in the sample after 4 hours. (Round your answer to the nearest whole number.)\[ \_\_\_ \text{ bacteria} \]*Image Description:* A scientist, in a lab setting, appears to be handling a laboratory apparatus, possibly related to the study or cultivation of bacterial samples.

Given that the bacteria Streptococcus pneumonia is the cause of many human diseases, the most common…

The bacteria Streptococcus pneumoniae (S. pneumoniae) is the cause of many human diseases, the most common being pneumonia. A culture of these bacteria initially has 10 bacteria and increases at a rate of 25% per hour. (a) Find the hourly growth factor a. a = Find an exponential model f(t) = Cat for the bacteria count in the sample, where t is measured in hours. f(t) = (b) Use the model you found to predict the number of bacteria in the sample after 4 hours. (Round your answer to the nearest whole number.) bacteria Laurence Gough/Shutterstock.com 2009

The bacteria Streptococcus pneumoniae (S. pneumoniae) is the cause of many human diseases, the most common being pneumonia. A culture of these bacteria initially has 10 bacteria and increases at a rate of 25% per hour. (a) Find the hourly growth factor a. a = Find an exponential model f(t) = Cat for the bacteria count in the sample, where t is measured in hours. f(t) = (b) Use the model you found to predict the number of bacteria in the sample after 4 hours. (Round your answer to the nearest whole number.) bacteria Laurence Gough/Shutterstock.com 2009

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Bacterial Growth of Streptococcus pneumoniae**

The bacteria *Streptococcus pneumoniae* (*S. pneumoniae*) is the cause of many human diseases, the most common being pneumonia. A culture of these bacteria initially has 10 bacteria and increases at a rate of 25% per hour.

---

**Tasks:**

**(a) Calculate the Hourly Growth Factor:**

Determine the growth factor per hour.
\[ a = \_\_\_ \]

**Exponential Model for Bacteria Count:**

Develop an exponential model $ f(t) = Ca^t $ for the bacteria count in the sample, where $ t $ is measured in hours.
\[ f(t) = \_\_\_ \]

**(b) Predict Bacteria Count After 4 Hours:**

Using the model found, estimate the number of bacteria in the sample after 4 hours. (Round your answer to the nearest whole number.)
\[ \_\_\_ \text{ bacteria} \]

*Image Description:* A scientist, in a lab setting, appears to be handling a laboratory apparatus, possibly related to the study or cultivation of bacterial samples.

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