1. The problem asks to find how much money was already in the account when Rachel started depositing money, i.e., the initial amount at time $0$ months. 2. We are given a table of time in months and corresponding money amounts: | Time (months) | 6 | 8 | 10 | 12 | |---------------|---|---|----|----| | Money (dollars) | 467 | 557 | 647 | 737 | 3. We assume the money grows linearly over time since the deposits are regular. 4. The linear model is $M = mt + b$ where $M$ is money, $t$ is time, $m$ is the rate of change (slope), and $b$ is the initial amount (intercept). 5. Calculate the slope $m$ using two points, for example $(6, 467)$ and $(12, 737)$: $$m = \frac{737 - 467}{12 - 6} = \frac{270}{6} = 45$$ 6. Use the slope and one point to find $b$: $$467 = 45 \times 6 + b$$ $$467 = 270 + b$$ $$b = 467 - 270 = 197$$ 7. Therefore, the initial amount of money in the account when Rachel started depositing was $\boxed{197}$ dollars.