Can I please get some help. Thank you 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.

Name: Can I please get some help. Thank you A bacteria culture is started wi
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Description: Can I please get some help. Thank you 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 a

Let P(n) be the population of bacteria after n hours can be modeled as, Pn=1+rnP0. To find the growth rate r, substitute n=4, P0=300 and P4=500 in Pn=1+rnP0, and simplify. Pt=1+rtP0P4=1+r4P0500=1+r4300500300=3001+r430053=1+r4ln53=ln1+r4ln5-ln3=4ln1+rln5-ln34=ln1+reln5-ln34=eln1+r=1+reln5-ln34-1=1+r-10.1362≈r Therefore, the growth rate is r=0.1362.To find the recursive formula for the number of bacteria, substitute r=0.1362 and P0=300 in Pn=1+rPn-1. Pn=1+rPn-1=1+0.1362Pn-1=1.1362Pn-1 Hence, the recursive formula for the population of bacteria is Pn=1.1362Pn-1.To find the explicit formula for the number of bacteria, substitute r=0.1362 and P0=300 in Pn=1+rnP0. Pn=1+rnP0=1+0.1362n300=3001.1362n Hence, the explicit formula for the population of bacteria is Pn=3001.1362n.To find the number of bacteria in one day, substitute 24 for n in the equation Pn=3001.1362n, and simplify. P24=3001.136224≈6427.41131≈6427 Thus, the population of bacteria will grow in one day is 6427.To estimate the time for triple the population, substitute 3P0 for Pn in the formula Pn=1.1362nP0, and solve for n. Pn=1.1362nP03P0=1.1362nP03P0P0=1.1362nP0P03=1.1362nln3=ln1.1362n=nln1.1362ln3ln1.1362=n8.6038≈n Hence, after 8.6 hours, the population will be 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?

. 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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.

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Can I please get some help. Thank you

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.

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