A scientist started with a sample of 8 cells. The sample increased as shown in the table.
Time (hours) Number of Cells
0 8
1 32
2 128
3 512
Assume that the pattern in the table continues. Which equation can be solved for t, the time in hours when the number of cells will reach 100,000?
A.
B.
C.
D.
Let's find a pattern in the data provided:
0 hours: 8 cells
1 hour: 32 cells (8 * 4)
2 hours: 128 cells (32 * 4)
3 hours: 512 cells (128 * 4)
From the pattern observed, the number of cells is increasing by a factor of 4 each hour.
To find the time when the number of cells will reach 100,000, we can set up the following equation:
8 * 4^t = 100,000
Solving for t:
4^t = 100,000 / 8
4^t = 12,500
t = log4(12,500)
Therefore, the correct equation for t in terms of the number of cells is:
t = log4(12,500)
The answer is not provided in the multiple choice options, so it seems like this question may have been flawed.