Let's go step-by-step to solve the problem.
### Step 1: Setting up the equation
Ms. Waker starts the fund with an initial deposit of \[tex]$5. Each week, the amount in the fund doubles. We want to find the number of weeks, \(x\), it will take for the fund to reach \$[/tex]1,280.
The initial deposit is \[tex]$5.
Each subsequent week, the amount doubles. So, the amount in the fund after \(x\) weeks is given by:
\[ 5 \times 2^x \]
We want this amount to be \$[/tex]1,280:
[tex]\[ 5 \times 2^x = 1,280 \][/tex]
### Step 2: Solving the equation for [tex]\(x\)[/tex]
To find [tex]\(x\)[/tex], we need to solve the equation:
[tex]\[ 5 \times 2^x = 1,280 \][/tex]
First, isolate [tex]\(2^x\)[/tex] by dividing both sides by 5:
[tex]\[ 2^x = \frac{1280}{5} \][/tex]
[tex]\[ 2^x = 256 \][/tex]
### Step 3: Determine [tex]\(x\)[/tex]
We recognize that [tex]\(256\)[/tex] is a power of [tex]\(2\)[/tex]:
[tex]\[ 256 = 2^8 \][/tex]
Therefore, we have:
[tex]\[ 2^x = 2^8 \][/tex]
[tex]\[ x = 8 \][/tex]
### Step 4: Verify which equation corresponds to the scenario
From our derivation, the correct equation is:
[tex]\[ 5 \times 2^x = 1,280 \][/tex]
Comparing this with the given options, we find that Option D:
[tex]\[ 5(2)^x = 1,280 ; x=8 \][/tex]
### Conclusion
The correct equation to find the number of weeks, [tex]\(x\)[/tex], for the fund to reach \$1,280 is given by:
[tex]\[ 5(2)^x = 1,280 \][/tex]
and it will take [tex]\( \boxed{8} \)[/tex] weeks to reach the class goal.
