Read Chapter 7 to help you complete the questions in this exercise.

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?

`# area of a circle # the equation to calculate the area of a circle is pi * radius^2 circle.area <- function(d){ pi * (d/2)^2 } # to use your new function circle.area(10) # [1] 78.53982 # to test on a vector of diameters # first create a vector with diameters ranging from 0 to 50 in steps of 10 cir.diam <- seq(from = 0, to = 50, by = 10) # test your function circle.area(cir.diam) # [1] 0.00000 78.53982 314.15927 706.85835 1256.63706 1963.49541`

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.”`far.cent <- function(a) { val <- (a - 32) * 5/9 print(paste("Fahrenheit: ", round(a, digits = 3), "oF", sep = " "), quote = FALSE) # round 3dp print(paste("Centigrade: ", round(val, digits = 3), "oC", sep = " "), quote = FALSE) # round 3dp } # alternative Fahrenheit to centigrade using cat function far.cent2 <- function(a) { val <- (a - 32) * 5/9 #calculation cat("Fahrenheit: ", round(a, digits = 3), "oF", "\n") # use cat function cat("Centigrade: ", round(val, digits = 3), "oC", "\n") }`

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.

`# Create a vector of normally distributed data # length 100, mean 35 and standard deviation of 29 vals <- rnorm(100, 35, 15) # create some norm dist data mean 35, sd = 15 summary.fun <- function(dat){ mymean <- round(mean(dat), digits = 4) # calc mean mymedian <- round(median(dat), digits = 4) # calc median mymin <- round(min(dat), digits = 4) # calc min mymax <- round(max(dat), digits = 4) # calc max print(paste("mean:", mymean, sep = " "), quote = FALSE) # print mean print(paste("median:", mymedian, sep = " "), quote = FALSE) # print median print(paste("range:", "from:", mymin, "to", mymax, sep = " "), quote = FALSE) dens <- density(dat) # estimate density curve hist(dat, main = "",type = "l",freq = FALSE) # plot histogram lines(dens, lty = 1, col = "red") # plot density curve } # use the function summary.fun(vals)`

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.`# calculate a median ourmedian <- function(x){ n <- length(x) if (n %% 2 == 1) # odd numbers sort(x)[(n + 1)/2] # find the middle number by adding 1 to length and div 2 else { # even numbers middletwo <- sort(x)[(n/2) + 0:1] #find the two middle numbers mean(middletwo) } } # use the function mydat <- sample(1:50, size = 10, replace = TRUE ) # our function ourmedian(mydat) # R median function median(mydat)`

- You are a population ecologist for the day and wish to investigate the properties of the Ricker model. The Ricker model is defined as:

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

(cont) Where

*N*is the population size at time_{t}*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.`# function to simulate Ricker model Ricker.model <- function(nzero, r, time, K = 1) { # sets initial parameters N <- numeric(time + 1) # creates a real vector of length time+1 to store values of Nt+1 N[1] <- nzero # sets initial population size in first element of N for (i in 1:time) { # loops over time N[i + 1] <- N[i] * exp(r * (1 - N[i]/K)) } Time <- 0:time # creates vector for x axis plot(Time, N, type = "o", xlim = c(0, time), xlab = "Time", ylab = "Population size (N)", main = paste("r =", r, sep = " ")) # plots output } # To run play around with the different parameters, especially r Ricker.model(nzero = 0.1, r = 1, time = 100)`

End of Exercise 6