To determine the correct equation and number of weeks it will take Ms. Walker's class to reach a balance of \$1,280, we will analyze the situation step by step.
1. Identify the initial deposit and the growth pattern:
- The initial deposit is \$5.
- Each week, the balance doubles, which means the growth factor is 2.
2. Set up the exponential growth equation:
- The balance \( B \) after \( x \) weeks can be modeled by the equation:
[tex]\[
B = 5 \times 2^x
\][/tex]
3. Set the equation equal to the goal amount of \$1,280:
- To find out when the balance will reach \$1,280, we set up the equation:
[tex]\[
5 \times 2^x = 1,280
\][/tex]
4. Solve for \( x \):
- To isolate \( x \), we need to rewrite the equation in a form where we can solve for \( x \).
- Divide both sides by 5:
[tex]\[
2^x = \frac{1,280}{5} \implies 2^x = 256
\][/tex]
- We know that \( 2^8 = 256 \). Therefore:
[tex]\[
x = 8
\][/tex]
5. Identify the correct answer choice:
- The equation that matches our model \( 5(2)^x = 1,280 \) and the number of weeks \( x = 8 \) is option C.
So, the correct answer is:
C. [tex]$5(2)^x=1,280 ; x=8$[/tex]
