Subjects algebra

Call Cost

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1. **State the problem:** We need to find the fixed connection fee and the cost per minute from the given graph of cost versus time. 2. **Identify the fixed connection fee:** The fixed connection fee is the cost when the call duration is zero minutes. From the graph, at 0 minutes, the cost is about 100 pence. So, the fixed connection fee is $100$ pence. 3. **Find the cost per minute:** The cost per minute is the slope of the line, which is the change in cost divided by the change in time. 4. **Calculate the slope:** From the graph, at 60 minutes, the cost is 600 pence, and at 0 minutes, the cost is 100 pence. $$\text{slope} = \frac{600 - 100}{60 - 0} = \frac{500}{60} = \frac{50}{6} \approx 8.33$$ So, the cost per minute is approximately $8.33$ pence. 5. **Summary:** - Fixed connection fee = $100$ pence - Cost per minute = $\frac{50}{6} \approx 8.33$ pence This means the total cost $C$ for $t$ minutes can be modeled by the linear equation: $$C = 100 + \frac{50}{6}t$$