For a constant-rate model, the intercept is the starting amount and the gradient is the change in the output per unit change in the input. State the units and the range over which the model is valid. Example A tank starts with 20 litres and fills at 6 litres per minute. Before it reaches its 80-litre capacity, V=20+6t, where t is minutes after filling starts. It reaches capacity when 20+6t=80, giving t=10 minutes. The line shown applies for 0 <= t 10. Extending it beyond that interval would predict more than the capacity unless another process, such as overflow, were specified.

For a constant-rate model, the intercept is the starting amount and the gradient is the change in the output per unit change in the input. State the units and the range over which the model is valid.

A tank starts with \(20\) litres and fills at \(6\) litres per minute. Before it reaches its \(80\)-litre capacity, \(V=20+6t\), where \(t\) is minutes after filling starts. It reaches capacity when \(20+6t=80\), giving \(t=10\) minutes.

The line shown applies for \(0\le t\le10\). Extending it beyond that interval would predict more than the capacity unless another process, such as overflow, were specified.

Linear models in context

Linear models in context