Problem $1$: Exponential Decay Curve Fitting

The population of bacteria in a culture decays over time according to the equation:

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P$($t$)=$P$\_\{0\}$ e$^\{-$k t$\}$

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Given experimental data of time $\backslash ($ t $\backslash )($hours$)$ and population $\backslash ($ P $\backslash ),$ write a MATLAB script to:

$1.$ Determine the initial population $\backslash ($ P$\_\{0\}\backslash )$ and the decay constant $\backslash ($ k $\backslash )$ using the least$-$squares method.

$2.$ Calculate and display the coefficient of determination $\backslash ($ R$^\{2\}\backslash ).$

$3.$ Plot the experimental data points and the best$-$fit exponential curve on the same graph, including proper labels and a legend.