Subjects algebra

Cost Time

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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.