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.
The pattern in the table shows that the number of cells is increasing by a factor of 4 each hour. We can represent this pattern with the equation:
Number of Cells = 8 * 4^t
We need to solve for t when the number of cells is 100,000:
100,000 = 8 * 4^t
12,500 = 4^t
To solve for t, we first need to express 4 as a power of 2:
4 = 2^2
So the equation becomes:
12,500 = (2^2)^t
12,500 = 2^(2t)
Now, we can rewrite 12,500 as a power of 2 by using logarithms:
log2(12,500) = 2t
log2(12,500) = log2(2^(2t))
log2(12,500) = 2t
Now, solve for t using logarithms:
2t = log2(12,500)
t = log2(12,500) / 2
t ≈ 7.4
Therefore, the equation that can be solved for t is:
D. t = (log2(12,500)) / 2