Question
In a lab experiment, a population of 300 bacteria is able to double every hour. Which equation matches the number of bacteria in the population after 2 hours?
Answer
Attempt 1 out of 3
Multiple Choice Answers
B, equals, 2, left parenthesis, 300, right parenthesis, left parenthesis, 300, right parenthesisB=2(300)(300)
B, equals, 300, left parenthesis, 2, right parenthesis, left parenthesis, 2, right parenthesis, left parenthesis, 2, right parenthesisB=300(2)(2)(2)
B, equals, 2, left parenthesis, 300, right parenthesis, squaredB=2(300)
2
B, equals, 300, left parenthesis, 2, right parenthesis, squaredB=300(2)
2
Answer
Attempt 1 out of 3
Multiple Choice Answers
B, equals, 2, left parenthesis, 300, right parenthesis, left parenthesis, 300, right parenthesisB=2(300)(300)
B, equals, 300, left parenthesis, 2, right parenthesis, left parenthesis, 2, right parenthesis, left parenthesis, 2, right parenthesisB=300(2)(2)(2)
B, equals, 2, left parenthesis, 300, right parenthesis, squaredB=2(300)
2
B, equals, 300, left parenthesis, 2, right parenthesis, squaredB=300(2)
2
Answers
GPT-4o mini
To model the growth of a population of bacteria that doubles every hour, we can use the exponential growth formula:
\[
B(t) = B_0 \cdot 2^t
\]
where:
- \(B(t)\) is the number of bacteria at time \(t\),
- \(B_0\) is the initial population (300 in this case),
- \(t\) is the time in hours.
After 2 hours (\(t = 2\)), the formula becomes:
\[
B(2) = 300 \cdot 2^2
\]
Calculating further, we have:
\[
B(2) = 300 \cdot (2 \cdot 2) = 300 \cdot 4 = 1200
\]
Now, let's look at the provided options:
1. \(B = 2(300)(300)\) - Incorrect, as this represents multiplying by 2 and then the initial population twice, which is not how doubling works.
2. \(B = 300(2)(2)(2)\) - This is correct because it represents the initial population multiplied by \(2\) three times, which reflects doubling every hour for 2 hours (300 multiplied by \(2^2\)).
3. \(B = 2(300)^2\) - Incorrect, as this formula does not correctly apply the doubling concept.
4. \(B = 300(2)^2\) - This is also correct since it effectively describes the population after doubling twice (300 multiplied by \(4\)).
Thus, the correct equations that match the number of bacteria in the population after 2 hours are:
- \(B = 300(2)(2)(2)\)
- \(B = 300(2)^2\)
Both of options 2 and 4 give correct values, but since option 2 describes the doubling with individual factors, it is accurate to note that option 4 directly expresses the result as \(B = 300 \cdot 4\). Depending on how the prompt wishes to interpret the expectation on format, either could be taken, but typically, you should pick the simpler and more direct formulation, which would be \(B = 300(2)^2\) or option 4.
So, the final answer should be:
**B = 300(2)^2**.
\[
B(t) = B_0 \cdot 2^t
\]
where:
- \(B(t)\) is the number of bacteria at time \(t\),
- \(B_0\) is the initial population (300 in this case),
- \(t\) is the time in hours.
After 2 hours (\(t = 2\)), the formula becomes:
\[
B(2) = 300 \cdot 2^2
\]
Calculating further, we have:
\[
B(2) = 300 \cdot (2 \cdot 2) = 300 \cdot 4 = 1200
\]
Now, let's look at the provided options:
1. \(B = 2(300)(300)\) - Incorrect, as this represents multiplying by 2 and then the initial population twice, which is not how doubling works.
2. \(B = 300(2)(2)(2)\) - This is correct because it represents the initial population multiplied by \(2\) three times, which reflects doubling every hour for 2 hours (300 multiplied by \(2^2\)).
3. \(B = 2(300)^2\) - Incorrect, as this formula does not correctly apply the doubling concept.
4. \(B = 300(2)^2\) - This is also correct since it effectively describes the population after doubling twice (300 multiplied by \(4\)).
Thus, the correct equations that match the number of bacteria in the population after 2 hours are:
- \(B = 300(2)(2)(2)\)
- \(B = 300(2)^2\)
Both of options 2 and 4 give correct values, but since option 2 describes the doubling with individual factors, it is accurate to note that option 4 directly expresses the result as \(B = 300 \cdot 4\). Depending on how the prompt wishes to interpret the expectation on format, either could be taken, but typically, you should pick the simpler and more direct formulation, which would be \(B = 300(2)^2\) or option 4.
So, the final answer should be:
**B = 300(2)^2**.