In MATLAB:

Ligands $($compounds that bind to specific molecules; for example, drugs, neurotransmitters, and hormones$)$ coming off of receptors obey exponential decay kinetics. Imagine receptors with ligands bound at an initial concentration $C_0=1uM($micromolar or ${10}^{-6}M)$ dissociating with a rate constant $k=1s^{-1}.$ Using MATLAB, plot $C(t)$ vs$.t$ from $0$ to $10$ seconds for this situation.

First, make a time vector from $t=0$ to $t=10s,$ with time steps of $0\mathrm{.}1s.$ Then use this time vector to define a concentration vector using the above equation. Use these two vectors to plot concentration as a function of time. Add $x-$ and $y-$axis labels $($be sure to include units!$)$ and add a title that includes your name and the due date. If you get stuck on any step, try googling your problem to get an idea of what command to use and what the appropriate syntax is$.$ Don't overthink it$!$ The whole code should be $5-10$ lines. We require each line of code to have a comment! This will help you understand what each code line does and help whoever is grading your code realize what you are trying to accomplish.

Save the figure as a $.$jpg and turn it in with the rest of your code.

Use this plot to study exponentials a bit. Use the "Data Tips" tool under the Tools tab at the top of the figure panel $($This may be called the "Cursor Tool" in Tolder versions of MATLAB$).$ You can now click on the curve and move along it $($using the arrow keys$)$ to read $x$ and $y$ values $-$ this is very handy. Figure out the half$-$life $($i$.$e$.,$ the time it takes for the concentration to fall to half of its initial value$).$ Use this half$-$life to calculate $.$ Use the rate constant to calculate $.$ Do these numbers agree?

$2.$ Use the cursor tool in MATLAB to find the percent concentration remaining after $1$ time constant. What is the concentration after $3-$time constants? $5$time constants? People often use $3-$time constants as a general rule for $95\%$ completion and $5-$time constants for $99\%$ completion. Do you see why?

$3.$ Be sure to show all your work, including screen shots of any cursor tool measurements