A pastry chef is heating a sugar syrup in order to make a tart glaze.

The temperature, ${\theta }^{\circ }\text{C}$, of the syrup after $t$ minutes can be modeled by the function

where $\mu \in \mathbb{R}$ is a constant.

1. Write down the initial temperature of the syrup.

2. The syrup must be removed from the heat when it has reached at least ${104}^{\circ }\text{C}$ and at most ${106}^{\circ }\text{C}$. Given that it takes $4$ minutes for the syrup to reach ${100}^{\circ }\text{C}$, how long does the temperature of the syrup remain in the required range?

For (b), the key is to find the value of $\mu$ by substituting $\theta =100,t=4$ into the model.

Give your answer to (b) in seconds, correct to $3$ significant figures.