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Select the correct answer.

Ms. Walker's class set up an online fund with a goal to raise \[tex]$1,280 to go on a field trip. Ms. Walker starts the fund by depositing \$[/tex]5. Each week the balance of the fund is twice the balance of the previous week.

Which equation can be used to find the number of weeks, [tex] x [/tex], after which the balance of the fund will reach \$1,280, and how many weeks will it take to reach the class goal?

A. [tex] 1,280 \left(\frac{1}{3}\right)^x = 2 ; x = 4 [/tex]
B. [tex] 2 (5)^\pi = 1,280 ; x = 5 [/tex]
C. [tex] 5(2)^x = 1,280 ; x = 8 [/tex]
D. [tex] 1,280 \left(\frac{1}{2}\right)^x = 5 ; x = 7 [/tex]



Answer :

GinnyAnswer
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]

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