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<h1 class="title toc-ignore">Exercise 6</h1>
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<p> </p>
<div id="exercise-6-basic-programming-in-r" class="section level2">
<h2>Exercise 6: Basic programming in R</h2>
<p> </p>
<p>Read <a href="https://intro2r.com/prog-r.html">Chapter 7</a> to help
you complete the questions in this exercise.</p>
<p> </p>
<p>1. Create a function to calculate the area of a circle. Test the
function by finding the area of a circle with a diameter of 3.4 cm. Can
you use it on a vector of data?</p>
<p> </p>
<p>2. Write a function to convert farenheit to centegrade (oC = (oF -
32) x 5/9). Get your function to print out your result in the following
format: “Farenheit : <em>value of oF</em> is equivalent to <em>value
oC</em> centigrade.”</p>
<p> </p>
<p>3. Create a vector of normally distributed data, of length 100, mean
35 and standard deviation of 15. Write a function to calculate the mean,
median, and range of the vector, print these values out with appropriate
labels. Also get the function to plot a histogram (as a proportion) of
the values and add a density curve.</p>
<p> </p>
<p>4. Write a function to calculate the median value of a vector of
numbers (yes I know there’s a <code>median()</code> function already but
this is fun!). Be careful with vectors of an even sample size, as you
will have to take the average of the two central numbers (hint: use
modulo %%2 to determine whether the vector is an odd or an even size).
Test your function on vectors with both odd and even sample sizes.</p>
<p> </p>
<p>5. You are a population ecologist for the day and wish to investigate
the properties of the <a
href="https://en.wikipedia.org/wiki/Ricker_model">Ricker model</a>. The
Ricker model is defined as:</p>
<p> </p>
<p><span class="math display">\[ N_{t+1} = N_{t} exp\left[r\left(1-
\frac{N_{t}}{K} \right) \right] \]</span></p>
<p> </p>
<p>5. (cont) Where <em>N<sub>t</sub></em> is the population size at time
<em>t</em>, <em>r</em> is the population growth rate and <em>K</em> is
the carrying capacity. Write a function to simulate this model so you
can conveniently determine the effect of changing <em>r</em> and the
initial population size N0. <em>K</em> is often set to 100 by default,
but you want the option of being able to change this with your function.
So, you will need a function with the following arguments; nzero which
sets the initial population size, <em>r</em> which will determine the
population growth rate, time which sets how long the simulation will run
for and <em>K</em> which we will initially set to 100 by default.</p>
<p> </p>
<p>End of Exercise 6</p>
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