A supplied continuous linear model of water remaining V is valid for 0 ≤ t ≤ 8 minutes. Its points are (2, 16.5) and (6, 9.5), with minutes first. Find the signed change rate and total at zero. Write a rule, check both points and complete the table. Explain what the negative rate means and whether remaining water is proportional to time.
| Time (minutes) | Water remaining (liters) |
|---|---|
| 0 | |
| 2 | 16.5 |
| 6 | 9.5 |
| 8 |
Rule, units and explanation; plot or describe the points
Linear Relationships Follow-up Check
For the same 0-to-8-minute domain, W = 17 − 0.75t gives water remaining in liters. Which has the greater signed change rate? Which loses more liters per minute? Compare totals at minutes 1 and 8 and find the equality time. Explain why greater starting water need not mean more water throughout the domain.
Your signed-rate and output comparisons
Someone uses your rule from problem 1 to announce an actual amount at minute 10. Explain what the stated model establishes and what an extension beyond minute 8 would require.
Your model-boundary explanation
Linear Relationships Follow-up Check
A constructed continuous linear Celsius-temperature model is valid for 0 ≤ t ≤ 6 minutes. It gives (1, −4) and (4, 2), with minutes first. Find its signed change rate, zero-time value and rule. Verify both points. What temperature does the model give at minute 3? Explain why a positive rate can go with a negative starting temperature.
Rate, zero-time value, rule and interpretation