1. **State the problem:** We have a table showing the number of minutes $t$ a computer is used and the total cost $C$ to use it. The values for $t$ are 0, 1, 2, and 3 minutes, but the costs $C$ are missing. We want to find the relationship between $C$ and $t$ and fill in the missing costs.
2. **Assume a linear cost model:** Usually, the total cost $C$ depends linearly on the time $t$, so we can write:
$$C = mt + b$$
where $m$ is the cost per minute and $b$ is the fixed starting cost.
3. **Determine $b$ (fixed cost):** When $t=0$ (no time used), the total cost $C$ should be $0$ if there is no fixed fee. So,
$$C = m \times 0 + b = b$$
Since no cost is given, we assume $b=0$.
4. **Determine $m$ (cost per minute):** Without cost data, we cannot find $m$ exactly. But if we assume the cost increases by a fixed amount each minute, then the cost for $t$ minutes is:
$$C = m t$$
5. **Fill in the table with a sample cost rate:** For example, if the cost is 2 units per minute, then:
- At $t=0$, $C=0$
- At $t=1$, $C=2 \times 1 = 2$
- At $t=2$, $C=2 \times 2 = 4$
- At $t=3$, $C=2 \times 3 = 6$
6. **Final formula:**
$$C = 2t$$
This formula can be adjusted if actual cost data is provided.
**Answer:** The total cost $C$ is proportional to the number of minutes $t$ used, with $C = 2t$ as an example.
Cost Time
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