MEPV$102$ Practical Example $3\mathrm{.}2-$ Carbon $14$ Dating MEPV$102$ Practical Example $3\mathrm{.}6-$ For loop examples

Use a For loop to solve the following problems:

a$)$ Create a table that converts inches to feet. Convert the values ranging between $0$ and $24$

inches $($with increments of $3)$ to feet.

b$)$ Consider the following matrix values:

$x=[45,23,17,34,85,33]$

By using a counter how many values are greater than $30?$

c$)$ Repeat the previous exercise, this time by using the find command.

d$)$ Use a For loop to sum the elements of the matrix in problem $2.$ Check your results with the

sum function. $($Use the HELP feature to assist you how to use sum$).$

e$)$ Use a For loop to create a vector containing the first $10$ elements in the alternating harmonic

series, i$.$e$.$

$\frac{1}{1},-\frac{1}{2},\frac{1}{3},-\frac{1}{4},\frac{1}{5}$dots$-\frac{1}{10}$ MEPV$102$ Practical Example $4\mathrm{.}2-$ Storing Planetary Data with Structure

Arrays

Structure arrays can be used much like a database. You can store numeric information, as well as character data or any of the other data types supported by MATLAB. Write a MATLAB program that will create a structure array from the information given in the table below. Your program should prompt the user to enter the data separately for the given planets and then store the information as a structure array. Make use of a WHILE loop to enter and store the data, and a SWITCH$/$CASE structure to check if the data has been entered correctly. Make use of the MENU function to control your loop and branching structure.

$\backslash$table$[[$Planet Name,$\backslash$table$[[$Mass$,$ in Earths$],[$Multiples$]],\backslash$table$[[$Length of Year, in$],[$Earths Years$]],\backslash$table$[[$Orbital Velocity,$],[$km$/$s$]]],[$Mercury$,0\mathrm{.}055,0\mathrm{.}24,47\mathrm{.}89],[$Venus$,0\mathrm{.}815,0\mathrm{.}62,35\mathrm{.}03],[$Earth$,1,1,29\mathrm{.}79],[$Mars$,0\mathrm{.}107,1\mathrm{.}88,24\mathrm{.}13],[$Jupiter$,318,11\mathrm{.}86,13\mathrm{.}06],[$Saturn$,95,29\mathrm{.}46,9\mathrm{.}64],[$Uranus$,15,84\mathrm{.}01,6\mathrm{.}81],[$Neptune$,17,164\mathrm{.}8,5\mathrm{.}43],[$Pluto$,0\mathrm{.}002,247\mathrm{.}7,4\mathrm{.}74]]$

A radioactive isotope of an element is a form of the element that is not stable. Instead it

spontaneously decays into another element over a period of time. Radioactive decay is an

exponential process. If $Q_0$ is the initial quantity of a radioactive substance at time $t=0,$ then

the amount of the substance which will be present at any time $t$ in the future is given by:

$Q(t)=Q_0{e}^{-t}$

where $($Lambda$)$ is the radioactive decay constant.

Because radioactive decay occurs at a known rate, it can be used as a clock to measure the

time that has elapsed since the decay started. If we know the initial amount of the

radioactive material $Q_0$ present in a sample and the amount of material $Q$ left at the current

time, we can solve for $t$ in the above mentioned equation to determine how long the decay

has been going on$.$ Equation $2\mathrm{.}1$ has practical applications in many areas of science. For

example, archaeologists use a radioactive clock based on carbon $14$ to determine the time

that has passed since a once living thing died. Carbon $14$ is continually taken into the body

while a plant or animal is living, so the amount of it present in the body at the time of death

is assumed to be known. The decay constant $$ of carbon $14$ is well known to be

$\frac{0\mathrm{.}00012097}{y}$ear. Write a MATLAB program that will prompt the user to enter the

percentage of carbon $14$ remaining in a sample and then calculates the age of the sample

from it$.$ Displays the results with the correct units by means of the display function in the

Command Window.