Question

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. 4 x t^8 = 100,000

B. 4 x 8^t = 100,000

C. 8 x t^4 = 100,000

D. 8 x 4^t = 100,000

Answer 1

To determine the correct equation that can be solved for \( t \) when the number of cells reaches 100,000, we first need to analyze the pattern in the data provided:

- When \( t = 0 \), the number of cells is \( 8 \).
- When \( t = 1 \), the number of cells is \( 32 \).
- When \( t = 2 \), the number of cells is \( 128 \).
- When \( t = 3 \), the number of cells is \( 512 \).

The pattern shows that the number of cells doubles every hour. Specifically:

- From \( 8 \) to \( 32 \) (which is \( 8 \times 4 \))
- From \( 32 \) to \( 128 \) (which is \( 32 \times 4 \))
- From \( 128 \) to \( 512 \) (which is \( 128 \times 4 \))

This indicates that the number of cells can be described as:

\[ N(t) = 8 \times 4^t \]

where \( N(t) \) is the number of cells at time \( t \).

To find the time \( t \) when the number of cells reaches \( 100,000 \), set up the equation:

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

Thus, the correct answer is:

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