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Answer :
To find the population of bacteria after 13 hours, we will use the formula:
[tex]\[ P_t = P_0 \cdot 2^{\frac{t}{d}} \][/tex]
where:
- [tex]\( P_0 = 94000 \)[/tex] is the initial population,
- [tex]\( t = 13 \)[/tex] is the time in hours,
- [tex]\( d = 10 \)[/tex] is the doubling time in hours,
- [tex]\( P_t \)[/tex] is the population after [tex]\( t \)[/tex] hours.
Now, let's break down the steps:
1. Identify the values:
- Initial population ([tex]\( P_0 \)[/tex]): 94000 bacteria
- Time elapsed ([tex]\( t \)[/tex]): 13 hours
- Doubling time ([tex]\( d \)[/tex]): 10 hours
2. Substitute these values into the formula:
[tex]\[ P_t = 94000 \cdot 2^{\frac{13}{10}} \][/tex]
3. Calculate the exponent:
- First, solve [tex]\( \frac{13}{10} = 1.3 \)[/tex].
4. Raise 2 to the power of 1.3:
- This computation gives approximately [tex]\( 2^{1.3} \approx 2.462 \)[/tex].
5. Multiply [tex]\( 94000 \)[/tex] by [tex]\( 2.462 \)[/tex]:
- [tex]\( 94000 \times 2.462 \approx 231455.88 \)[/tex].
6. Round to the nearest whole number:
- The population after 13 hours, rounded to the nearest whole number, is 231455.
Therefore, the population of bacteria in the culture after 13 hours is approximately 231,455.
[tex]\[ P_t = P_0 \cdot 2^{\frac{t}{d}} \][/tex]
where:
- [tex]\( P_0 = 94000 \)[/tex] is the initial population,
- [tex]\( t = 13 \)[/tex] is the time in hours,
- [tex]\( d = 10 \)[/tex] is the doubling time in hours,
- [tex]\( P_t \)[/tex] is the population after [tex]\( t \)[/tex] hours.
Now, let's break down the steps:
1. Identify the values:
- Initial population ([tex]\( P_0 \)[/tex]): 94000 bacteria
- Time elapsed ([tex]\( t \)[/tex]): 13 hours
- Doubling time ([tex]\( d \)[/tex]): 10 hours
2. Substitute these values into the formula:
[tex]\[ P_t = 94000 \cdot 2^{\frac{13}{10}} \][/tex]
3. Calculate the exponent:
- First, solve [tex]\( \frac{13}{10} = 1.3 \)[/tex].
4. Raise 2 to the power of 1.3:
- This computation gives approximately [tex]\( 2^{1.3} \approx 2.462 \)[/tex].
5. Multiply [tex]\( 94000 \)[/tex] by [tex]\( 2.462 \)[/tex]:
- [tex]\( 94000 \times 2.462 \approx 231455.88 \)[/tex].
6. Round to the nearest whole number:
- The population after 13 hours, rounded to the nearest whole number, is 231455.
Therefore, the population of bacteria in the culture after 13 hours is approximately 231,455.
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