To find the equation that describes the growth of the cells over time, let's look at the pattern in the data provided:
- At 0 hours: 8 cells
- At 1 hour: 32 cells
- At 2 hours: 128 cells
- At 3 hours: 512 cells
We can observe that the number of cells increases by a factor of 4 for each hour:
- From 0 to 1 hour: \(8 \times 4 = 32\)
- From 1 to 2 hours: \(32 \times 4 = 128\)
- From 2 to 3 hours: \(128 \times 4 = 512\)
Thus, the number of cells at any time \(t\) can be modeled by the equation:
\[ \text{Number of Cells} = 8 \times 4^t \]
We want to find the time \(t\) when the number of cells reaches 100,000. Therefore, we set up the equation:
\[ 8 \times 4^t = 100,000 \]
Now, looking at the options provided, the correct equation is:
D. \(8 \times 4^t = 100,000\).