Question

Question 11 (4 points)

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Jennifer's bank account is modeled by the equation y=12x+45where x represents the number of weeks and y equals the total balance

William's bank account, after weekly deposits, is shown in the following table.

Week: 0,1,2,3,4
Balance:30,44,5,72,86

Who started with more money in their account? Justify your reasoning. You must show ALL work to earn full credit.

Answer 1

To find out who started with more money in their account, we need to analyze both accounts according to the information given.

### Step 1: Analyzing Jennifer's Account
Jennifer's bank account balance is modeled by the equation:
\[ y = 12x + 45 \]
where \( x \) is the number of weeks and \( y \) is the total balance.

To find out how much money Jennifer started with (when \( x = 0 \)), we substitute \( x = 0 \) in the equation:

\[
y = 12(0) + 45
\]
\[
y = 0 + 45
\]
\[
y = 45
\]

So, Jennifer started with **$45**.

### Step 2: Analyzing William's Account
Now let's look at William's account from the given data:

- Week 0: Balance = 30
- Week 1: Balance = 44
- Week 2: Balance = 5 (This appears to be an error in the data as it indicates a withdrawal or mistake since the balance should generally increase)
- Week 3: Balance = 72
- Week 4: Balance = 86

From the table, the balance at Week 0 for William is **$30**.

### Step 3: Comparing Initial Balances
Now we compare the initial balances of both accounts:

- **Jennifer's initial balance:** $45
- **William's initial balance:** $30

### Conclusion
Jennifer started with more money in her account. To summarize the reasoning:

- We calculated Jennifer's initial balance using the equation \( y = 12x + 45 \) by substituting \( x = 0 \).
- William’s initial balance was taken directly from the provided data, which indicated $30.

Therefore, \( 45 > 30 \), which shows Jennifer started with more money.