Video: Recognizing Situations in Which a Quantity Changes at a Constant Rate per Unit Interval Relative to Another

The temperature decreases by 1°C every 2 hours from 6 pm to 5 am. Can this be represented by a linear or an exponential decay model?

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Video Transcript

The temperature decreases by one degree Celsius every two hours from 6 pm to 5 am. Can this be represented by a linear or exponential decay model?

First, let’s consider the differences between linear decay and exponential decay. In linear decay, the rate of decay is constant. In exponential decay, the rate of decay is proportional to the amount present. To determine which type this is, let’s see if we can model what’s happening with our temperature.

Our temperature decrease is a function of time. We don’t know what the temperature is at 6 pm. But we do know that, two hours later, it was decreased by one degree. At 10 pm, it was one degree less than the temperature at 8 pm. At 12 pm, we would decrease by one degree again. We can sketch a line through these points. What we recognise by this line is that the rate of change is constant. Every two hours, the temperature is decreased by one degree.

This event would be represented by a linear decay model.

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