A scientist started with a sample of 8 cells. The sample increased as shown in the table.

Question

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. 4 x t^8 = 100,000

B. 4 x 8^t = 100,000

C. 8 x t^4 = 100,000

D. 8 x 4t = 100,000

Answer 1

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. \(8 \times 4^t = 100,000\).