Read Chapter 7 to help you complete the questions in this exercise.
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?
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.”
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.
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.
5. You are a population ecologist for the day and wish to investigate the properties of the Ricker model. The Ricker model is defined as:
\[ N_{t+1} = N_{t} exp\left[r\left(1- \frac{N_{t}}{K} \right) \right] \]
5. (cont) Where Nt 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.
End of Exercise 6