To determine the equation that can be solved for \( t \) when the number of cells reaches 100,000, we first need to analyze the growth pattern of the cells based on the data provided:
- At 0 hours: 8 cells
- At 1 hour: 32 cells
- At 2 hours: 128 cells
- At 3 hours: 512 cells
To identify the pattern, we can see that each hour, the number of cells is multiplied by 4:
- From 8 to 32: \( 8 \times 4 = 32 \)
- From 32 to 128: \( 32 \times 4 = 128 \)
- From 128 to 512: \( 128 \times 4 = 512 \)
This demonstrates that the growth of the number of cells is exponential. We can express the number of cells \( N(t) \) at time \( t \) using the following formula:
\[ N(t) = 8 \times 4^t \]
We are tasked with finding out when \( N(t) \) will equal 100,000:
\[ 8 \times 4^t = 100000 \]
To solve for \( t \), we can rearrange the equation:
\[ 4^t = \frac{100000}{8} \]
Now, simplifying \( \frac{100000}{8} \):
\[ 4^t = 12500 \]
Thus, the equation that can be solved for \( t \) is:
\[ 4^t = 12500 \]
This is the equation that represents when the number of cells will reach 100,000. You can analyze the options you've provided (A, B, C, D) to find the equivalent representation of this equation. If you have specific equations listed as options, please provide them, so I can assist you in identifying the correct one.