Question
The number of cells in a petri dish triples every hour according to the equation N(t) = 80(3)t
where N(t) represents the number of cells after t hours. Match the following numbers of cells to the corresponding time.
174960 - __
58320 - __
Responses
7 hours
6 hours
5 hours
where N(t) represents the number of cells after t hours. Match the following numbers of cells to the corresponding time.
174960 - __
58320 - __
Responses
7 hours
6 hours
5 hours
Answers
GPT-4o mini
To find the corresponding time for each number of cells using the equation \( N(t) = 80(3^t) \), we can substitute each time value into the equation and see if it matches one of the given cell counts.
Let's calculate the number of cells for \( t = 5, 6, \) and \( 7 \):
1. **For \( t = 5 \):**
\[
N(5) = 80(3^5) = 80 \cdot 243 = 19440
\]
2. **For \( t = 6 \):**
\[
N(6) = 80(3^6) = 80 \cdot 729 = 58320
\]
3. **For \( t = 7 \):**
\[
N(7) = 80(3^7) = 80 \cdot 2187 = 174960
\]
Now, we can match the numbers of cells to the corresponding times:
- 174960 - **7 hours**
- 58320 - **6 hours**
- 19440 - **5 hours** (not in your list, but here for completeness)
So, the final matching is:
- 174960 - 7 hours
- 58320 - 6 hours
Let's calculate the number of cells for \( t = 5, 6, \) and \( 7 \):
1. **For \( t = 5 \):**
\[
N(5) = 80(3^5) = 80 \cdot 243 = 19440
\]
2. **For \( t = 6 \):**
\[
N(6) = 80(3^6) = 80 \cdot 729 = 58320
\]
3. **For \( t = 7 \):**
\[
N(7) = 80(3^7) = 80 \cdot 2187 = 174960
\]
Now, we can match the numbers of cells to the corresponding times:
- 174960 - **7 hours**
- 58320 - **6 hours**
- 19440 - **5 hours** (not in your list, but here for completeness)
So, the final matching is:
- 174960 - 7 hours
- 58320 - 6 hours