(Solved): Coding problem: (Use PYTHON codes) HW1_2 If a hot liquid in a container is left to cool, its tempe ...

Coding problem: (Use PYTHON codes) HW1_2 If a hot liquid in a container is left to cool, its temperature will gradually approach room temperature. The temperature of the liquid is expected to follow the mathematical model \( \mathrm{T}=\mathrm{A}+\mathrm{B} \mathrm{e}^{\mathrm{mt}} \), where \( \mathrm{A}=30 \mathrm{C}, \mathrm{B}=40 \mathrm{C}, \mathrm{m}=-0.276 \mathrm{~min}^{-1} \) The following data was also obtained in an experiment studying this phenomenon. In the same figure window, plot the data points along with the mathematical model. Include labels \& title. NOTE: Use a continuous plot to represent the model and discrete point plot to represent the data. HW1_3 problem 3.13/4.1 The 'divide and average' method, an old-time iterative method for approximating the square root of any positive number \( a \), can be formulated as \( x_{i+1}=\frac{x_{i}+a / x_{i}}{2} \). Using this method write a PYTHON code (script) to find the square root of 15 correct to 4 significant figures and use a print statement to write your final answer to the screen. Hints: 1. Note that \( a=15 \) in this case as you are trying to find the square root of 15 . Start with an initial value of \( x_{0} \). An intelligent initial guess can be \( x_{0}=\mathrm{a} / 2 \). 2. Use a while loop to calculate the updated value of \( x \) according to the above iterative formula \[ x_{i+1}=\frac{x_{i}+a / x_{i}}{2} \]