. A bacteria culture is started with 300 bacteria. After 4 hours, the population has grown to 500 bacteria. If the population grows exponentially, a. Write a recursive formula for the number of bacteria b. Write an explicit formula for the number of bacteria c. If this trend continues, how many bacteria will there be in 1 day? d. How long does it take for the culture to triple in size?

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A bacteria culture is started with 300 bacteria. After 4 hours, the population has grown to 500 bacteria. If the population grows exponentially:

a. Write a recursive formula for the number of bacteria.  
b. Write an explicit formula for the number of bacteria.  
c. If this trend continues, how many bacteria will there be in 1 day?  
d. How long does it take for the culture to triple in size?
Transcribed Image Text:A bacteria culture is started with 300 bacteria. After 4 hours, the population has grown to 500 bacteria. If the population grows exponentially: a. Write a recursive formula for the number of bacteria. b. Write an explicit formula for the number of bacteria. c. If this trend continues, how many bacteria will there be in 1 day? d. How long does it take for the culture to triple in size?
**Exponential Growth of Bacteria Culture: A Study**

A bacteria culture is initiated with a population of 300 bacteria. After a period of 4 hours, this population increases to 500 bacteria. Assuming the population grows exponentially, we are tasked with the following:

a. **Recursive Formula for the Number of Bacteria:**
   - Develop a recursive formula to represent this growth pattern over time.

b. **Explicit Formula for the Number of Bacteria:**
   - Create an explicit formula that models this exponential growth.

c. **Future Prediction:**
   - Calculate how many bacteria will exist after 1 day (24 hours), given the current trend continues.

d. **Tripling Time Calculation:**
   - Determine the time required for the bacteria culture to increase to three times its initial size.

These questions are designed to enhance understanding of exponential functions and their applications in modeling biological growth processes.
Transcribed Image Text:**Exponential Growth of Bacteria Culture: A Study** A bacteria culture is initiated with a population of 300 bacteria. After a period of 4 hours, this population increases to 500 bacteria. Assuming the population grows exponentially, we are tasked with the following: a. **Recursive Formula for the Number of Bacteria:** - Develop a recursive formula to represent this growth pattern over time. b. **Explicit Formula for the Number of Bacteria:** - Create an explicit formula that models this exponential growth. c. **Future Prediction:** - Calculate how many bacteria will exist after 1 day (24 hours), given the current trend continues. d. **Tripling Time Calculation:** - Determine the time required for the bacteria culture to increase to three times its initial size. These questions are designed to enhance understanding of exponential functions and their applications in modeling biological growth processes.
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