exercise_6.Rmd

---
title: "Exercise 6"
output: 
  html_document:
   toc: false
---

```{r setup, echo=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE, eval = FALSE, cache = FALSE)
```

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## Exercise 6: Basic programming in R

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Read [Chapter 7](https://intro2r.com/prog-r.html) to help you complete the questions in this exercise.

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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?

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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 : *value of oF* is equivalent to *value oC* centigrade."

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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.

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4\. Write a function to calculate the median value of a vector of numbers (yes I know there's a ```median()``` 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. 

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5\. You are a population ecologist for the day and wish to investigate the properties of the [Ricker model](https://en.wikipedia.org/wiki/Ricker_model). The Ricker model is defined as:

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$$ N_{t+1} = N_{t} exp\left[r\left(1- \frac{N_{t}}{K} \right) \right] $$

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5\. (cont) Where *N~t~* is the population size at time *t*, *r* is the population growth rate and *K* is the carrying capacity. Write a function to simulate this model so you can conveniently determine the effect of changing *r* and the initial population size N0. *K* 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, *r* which will determine the population growth rate, time which sets how long the simulation will run for and *K* which we will initially set to 100 by default.

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End of Exercise 6