To determine the number of weeks it will take for the balance of the fund to reach \[tex]$1,280, we need to set up the correct equation and then solve for \( x \).
1. Identifying the initial amount and growth rate:
- The initial amount, \( S \), is \$[/tex]5.
- Each week, the balance is doubled, meaning it's multiplied by 2.
2. Setting up the correct exponential equation:
- We know that the fund balance grows exponentially as [tex]\( S \cdot 2^x \)[/tex], where [tex]\( S \)[/tex] is the starting amount, and [tex]\( x \)[/tex] is the number of weeks.
- Given that the goal is \[tex]$1,280, the equation we need is:
\[
5 \cdot 2^x = 1,280
\]
3. Solving for \( x \):
- To solve for \( x \), we need to isolate \( x \) in the equation.
- Divide both sides of the equation by 5 to simplify:
\[
2^x = \frac{1,280}{5}
\]
\[
2^x = 256
\]
- Now, we identify the power of 2 that equals 256:
\[
2^x = 2^8
\]
\[
x = 8
\]
Thus, the equation that represents the situation correctly is:
\[
5 \cdot 2^x = 1,280
\]
And it will take 8 weeks for the balance to reach \$[/tex]1,280.
Therefore, the correct answer is:
C. [tex]\( 5(2)^x = 1,280 ; x = 8 \)[/tex]
