In this programming exercise, you will write programs to plot a series of functions while changing a numerical parameter.

Instructions:

$1.$ Write a program that plots the following exponential decay of a radioactive substance can be modeled by the following equation:

N$($t$)=$ Noe$-*$

Where:

N$($t$)$ is the number of radioactive atoms at time t$.$

No is the initial number of radioactive atoms at t $=0.$

$1$ is the decay constant, which characterizes the rate of decay of the substance. t is time in seconds.

Write a Python program that plots the radioactive decay of a substance using the function

N$$t$=$Noe$-^$

for a range of values of $1.$ Choose a suitable range of $1$ values, such as $1=0\mathrm{.}01,0\mathrm{.}1,1\mathrm{.}0,10\mathrm{.}0.$

Customize your plot with the following specifications:

$$ Use different line colors or styles for each curve to distinguish them clearly.

$$ Label each curve with the corresponding $1$ value to indicate which decay rate it represents.

$$ Add a title to the plot $($e$.$g$.,$ "Radioactive Decay with Varying $1").$

$$ Label the x$-$axis as "Time $($s$)"$ and the y$-$axis as "Number of Radioactive Atoms."

$$ Create a legend to identify each curve.

$$ Save the plot as a high$-$resolution image $($e$.$g$.,$ PNG or JPG$).$

$$ Display the plot on the screen.

$$ Write comments in your code to explain the purpose of each section and any significant steps you took.

$$ Use appropriate Python libraries for plotting, such as Matplotlib.