Question
Ms. Hwang's biology class is observing the growth of bacteria. They start with 30 bacteria and the amount of bacteria doubles every day.
PART A
Which of the following equations can Ms. Hwang use to determine how many days it will take for there to be 480 bacteria?
In how many days will there be 480 bacteria?
PART A
Which of the following equations can Ms. Hwang use to determine how many days it will take for there to be 480 bacteria?
In how many days will there be 480 bacteria?
Answers
GPT-4o mini
To find out how many days it will take for the number of bacteria to grow to 480, you can use the formula for exponential growth. Since the bacteria double each day, the number of bacteria can be modeled by the equation:
\[
N(t) = N_0 \times 2^t
\]
where:
- \(N(t)\) is the number of bacteria at time \(t\),
- \(N_0\) is the initial number of bacteria,
- \(t\) is the number of days.
In Ms. Hwang's case:
- \(N_0 = 30\),
- We want to find \(t\) when \(N(t) = 480\).
So, we set up the equation:
\[
480 = 30 \times 2^t
\]
To solve for \(t\), first divide both sides by 30:
\[
16 = 2^t
\]
Now, we can express 16 as a power of 2:
\[
16 = 2^4
\]
Thus, we have:
\[
2^t = 2^4
\]
Since the bases are the same, we can equate the exponents:
\[
t = 4
\]
Therefore, it will take Ms. Hwang 4 days for there to be 480 bacteria.
\[
N(t) = N_0 \times 2^t
\]
where:
- \(N(t)\) is the number of bacteria at time \(t\),
- \(N_0\) is the initial number of bacteria,
- \(t\) is the number of days.
In Ms. Hwang's case:
- \(N_0 = 30\),
- We want to find \(t\) when \(N(t) = 480\).
So, we set up the equation:
\[
480 = 30 \times 2^t
\]
To solve for \(t\), first divide both sides by 30:
\[
16 = 2^t
\]
Now, we can express 16 as a power of 2:
\[
16 = 2^4
\]
Thus, we have:
\[
2^t = 2^4
\]
Since the bases are the same, we can equate the exponents:
\[
t = 4
\]
Therefore, it will take Ms. Hwang 4 days for there to be 480 bacteria.