The number of cells in a petri dish triples every hour according to the equation N(t) = 80(3)t

Question

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

Answer 1

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