To determine which equation can be used to find the number of weeks, [tex]$x$[/tex], after which the balance of the fund will reach [tex]$\$[/tex]1,280[tex]$, we need to understand the situation described.
Ms. Walker initially deposits $[/tex]\[tex]$5$[/tex] into the fund. Each week, the balance of the fund doubles, meaning it is 2 times the balance of the previous week.
Let's denote the balance of the fund by [tex]$B$[/tex]. The initial balance is:
[tex]\[ B_0 = 5 \][/tex]
After 1 week, the balance will be:
[tex]\[ B_1 = 5 \times 2 \][/tex]
After 2 weeks, the balance will be:
[tex]\[ B_2 = 5 \times 2^2 \][/tex]
Generally, after [tex]$x$[/tex] weeks, the balance [tex]$B_x$[/tex] will be:
[tex]\[ B_x = 5 \times 2^x \][/tex]
We want to find [tex]$x$[/tex] when the balance reaches [tex]$\$[/tex]1,280[tex]$. So we set up the equation:
\[ 5 \times 2^x = 1,280 \]
We need to solve for $[/tex]x[tex]$.
The correct equation is:
\[ 5 \left(2\right)^x = 1,280 \]
Now, to find the value of $[/tex]x[tex]$, we solve the equation as follows:
1. Divide both sides by 5:
\[ 2^x = \frac{1,280}{5} \]
\[ 2^x = 256 \]
2. Recognize that $[/tex]256 = 2^8[tex]$, so:
\[ 2^x = 2^8 \]
This implies:
\[ x = 8 \]
Thus, the number of weeks it will take to reach the goal of $[/tex]\[tex]$1,280$[/tex] is:
[tex]\[ x = 8 \][/tex]
Therefore, the correct answer is:
A. [tex]\(5(2)^x=1,280 ; x=8\)[/tex]
