ENV567_ProblemSet_1_MGalindo
Maureen_Galindo
1/28/2020
1. Install the ISwR R package. Write the built-in dataset thuesen to a tab-separated textfile. View it with a text editor. Change the NA to . (period), and read the changed fileback into R.
#install ISwR
#install.packages("ISwR")
library(ISwR)
#call built-in data "thuesen"
head(thuesen)## blood.glucose short.velocity
## 1 15.3 1.76
## 2 10.8 1.34
## 3 8.1 1.27
## 4 19.5 1.47
## 5 7.2 1.27
## 6 5.3 1.49write.table(thuesen, file = "results", quote = F, col.names = T, row.names = T, sep = "\t")
#open in text editor and manually change NA value to "." resave as "resultsfinal"
read.table("resultsfinal.txt")## blood.glucose short.velocity
## 1 15.3 1.76
## 2 10.8 1.34
## 3 8.1 1.27
## 4 19.5 1.47
## 5 7.2 1.27
## 6 5.3 1.49
## 7 9.3 1.31
## 8 11.1 1.09
## 9 7.5 1.18
## 10 12.2 1.22
## 11 6.7 1.25
## 12 5.2 1.19
## 13 19.0 1.95
## 14 15.1 1.28
## 15 6.7 1.52
## 16 8.6 .
## 17 4.2 1.12
## 18 10.3 1.37
## 19 12.5 1.19
## 20 16.1 1.05
## 21 13.3 1.32
## 22 4.9 1.03
## 23 8.8 1.12
## 24 9.5 1.72. The exponential growth of a population is described by this mathematical function:
Nt = N0 e^rt where Nt is the population size at time t, N0 is the initial population size, and r is the rateof growth or reproductive rate. Write an exponential growth function in R that alsogenerates a plot with time on the x axis and Nt on the y axis. Using that function createplots for 20 days assuming an initial population size of 10 individuals under three growthrate scenarios (0.5, 0.8, -0.1).
t<-1:20
r1<-(0.5)
r2<-(0.8)
r3<-(-0.1)
line0.5 <-(10*exp(r1*t))
line0.8 <-(10*exp(r2*t))
lineneg0.1 <-(10*exp(r3*t))
# plot the first curve by calling plot() function
# First curve is plotted
plot(t, line0.5, type="o", col="blue", pch="o", lty=1, ylim=c(0,1000), xlab = "Population Total", ylab = "Time (Days)" )
# Add second curve to the same plot by calling points() and lines()
# Use symbol '*' for points.
points(t, line0.8, col="red", pch="*")
lines(t, line0.8, col="red",lty=2)
# Add Third curve to the same plot by calling points() and lines()
# Use symbol '+' for points.
points(t, lineneg0.1, col="green",pch="+")
lines(t, lineneg0.1, col="green", lty=3)
3. Under highly favorable conditions, populations grow exponentially. Howeverresources will eventually limit population growth and exponential growth cannotcontinue indefinitely. This phenomenon is described by the logistic growth function:
Nt=K*N0/(N0+(K−N0)e^−rt) where K is the carrying capacity. Write a logistic growth function in R that alsogenerates a plot with time on the x axis and Nt on the y axis. Using that function createplots for 20 days assuming an initial population size of 10 individuals and a carryingcapacity of 1,000 individuals under three growth rate scenarios (0.5, 0.8, 0.4).
t<-1:20
r1<-(0.5)
r2<-(0.8)
r3<-(0.4)
line0.5 <-(1000*10)/(10+(1000-10)*exp(-r1*t))
line0.8 <-(1000*10)/(10+(1000-10)*exp(-r2*t))
line0.4 <-(1000*10)/(10+(1000-10)*exp(-r3*t))
# plot the first curve by calling plot() function
# First curve is plotted
plot(t, line0.5, type="o", col="blue", pch="o", lty=1, ylim=c(0,1100), xlab = "Population Total", ylab = "Time (days)" )
# Add second curve to the same plot by calling points() and lines()
# Use symbol '*' for points.
points(t, line0.8, col="red", pch="*")
lines(t, line0.8, col="red",lty=2)
# Add Third curve to the same plot by calling points() and lines()
# Use symbol '+' for points.
points(t, line0.4, col="green",pch="+")
lines(t, line0.4, col="green", lty=3)
4. Write a function (sum_n) that for any given value, say n, computes the sum of theintegers from 1 to n (inclusive). Use the function to determine the sum of integers from 1to 5,000.
n=5000
sum_n <- sum(1:n)
print(sum_n)## [1] 125025005. Write a function (sqrt_round) that takes a number x as input, takes the square root,rounds it to the nearest whole number and then returns the result.
x = 5
sqrt_round <- round(sqrt(x), 0)
print(sqrt_round)## [1] 2