Question

A scientist started witha 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?

(1 point)
Responses

4×t8=100,000
4×t8=100,000

8×4t=100,000
8 times 4 to the t th power is equal to 100 comma 000

8×t4=100,000
8×t4=100,000

4×8t=100,000

Answer 1

To find the equation that can be solved for \( t \), we first need to analyze the pattern in the table.

Starting with 8 cells, the sample doubles every hour. Observing the number of cells at each hour:

- At \( t = 0 \), the number of cells is \( 8 \).
- At \( t = 1 \), the number of cells is \( 32 \) (which is \( 8 \times 4^1 \)).
- At \( t = 2 \), the number of cells is \( 128 \) (which is \( 8 \times 4^2 \)).
- At \( t = 3 \), the number of cells is \( 512 \) (which is \( 8 \times 4^3 \)).

From this, we can see that the number of cells at time \( t \) follows the equation:

\[
\text{Number of Cells} = 8 \times 4^t
\]

We want to find \( t \) when the number of cells reaches \( 100,000 \):

\[
8 \times 4^t = 100,000
\]

Thus, the correct equation that can be solved for \( t \) is:

**8×4^t=100,000**

So, the correct response is:

**8 times 4 to the t th power is equal to 100,000**.