We appreciate your visit to A culture of bacteria has an initial population of 4800 and doubles every 9 hours Using the formula tex P t P 0 times 2. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the population of bacteria after 14 hours, we can use the formula for exponential growth:
[tex]\[ P(t) = P_0 \times 2^{(t/d)} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population after time [tex]\( t \)[/tex],
- [tex]\( P_0 \)[/tex] is the initial population,
- [tex]\( t \)[/tex] is the time in hours,
- [tex]\( d \)[/tex] is the doubling time in hours.
Given values:
- Initial population, [tex]\( P_0 = 4800 \)[/tex] bacteria,
- Doubling time, [tex]\( d = 9 \)[/tex] hours,
- Time after which we want to find the population, [tex]\( t = 14 \)[/tex] hours.
Now, substitute these values into the formula:
1. Calculate the exponent [tex]\((t/d)\)[/tex]:
[tex]\[ \frac{t}{d} = \frac{14}{9} \approx 1.5556 \][/tex]
2. Raise 2 to the power calculated in step 1:
[tex]\[ 2^{1.5556} \approx 2.93767 \][/tex]
3. Multiply the initial population by the result from step 2:
[tex]\[ P(t) = 4800 \times 2.93767 \approx 14109.4511 \][/tex]
After calculating, we round this number to the nearest whole number:
- The nearest whole number is 14109.
Therefore, the population of the bacteria after 14 hours will be approximately 14,109 bacteria.
[tex]\[ P(t) = P_0 \times 2^{(t/d)} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population after time [tex]\( t \)[/tex],
- [tex]\( P_0 \)[/tex] is the initial population,
- [tex]\( t \)[/tex] is the time in hours,
- [tex]\( d \)[/tex] is the doubling time in hours.
Given values:
- Initial population, [tex]\( P_0 = 4800 \)[/tex] bacteria,
- Doubling time, [tex]\( d = 9 \)[/tex] hours,
- Time after which we want to find the population, [tex]\( t = 14 \)[/tex] hours.
Now, substitute these values into the formula:
1. Calculate the exponent [tex]\((t/d)\)[/tex]:
[tex]\[ \frac{t}{d} = \frac{14}{9} \approx 1.5556 \][/tex]
2. Raise 2 to the power calculated in step 1:
[tex]\[ 2^{1.5556} \approx 2.93767 \][/tex]
3. Multiply the initial population by the result from step 2:
[tex]\[ P(t) = 4800 \times 2.93767 \approx 14109.4511 \][/tex]
After calculating, we round this number to the nearest whole number:
- The nearest whole number is 14109.
Therefore, the population of the bacteria after 14 hours will be approximately 14,109 bacteria.
Thanks for taking the time to read A culture of bacteria has an initial population of 4800 and doubles every 9 hours Using the formula tex P t P 0 times 2. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
