Math Problem Statement
tuliskan progranya
tuliskan progranya
Solution
The image you uploaded contains code written in R for generating a plot using ggplot2
and overlaying exponential curves in a base plot. Below is the transcription of the R code from the image:
rggplot(data=NULL, aes(x=factor(kelas_interval_exp), y=jumlah_exp, fill=rentang_exp)) + geom_bar(stat="identity") + xlab("Kelas Interval") + ylab("Jumlah") + ggtitle("Grafik Frekuensi Batang") + geom_text(aes(y=jumlah_exp/1.3, label=jumlah_exp)) + theme(plot.title = element_text(size = 12, face = "bold", colour = "darkblue", vjust = 3, hjust=0.5)) + labs(fill="Kelas Interval") + scale_fill_manual(values = c(heat.colors(length(jumlah_exp)))) y_exp <- dexp(x_exp, rate=3) plot(x_exp, y_exp, col="red") curve(dexp(x, rate=3), xlim = c(0.2, 5), col="blue") curve(dexp(x, rate=2), xlim = c(0.2, 5), col="blue", add=TRUE) curve(dexp(x, rate=1), xlim = c(0.1, 5), col="green", add=TRUE) curve(dexp(x, rate=1/2), xlim = c(0.1, 5), col="green", add=TRUE) curve(dexp(x, rate=1/3), xlim = c(0.1, 5), col="orange", add=TRUE) curve(dexp(x, rate=1/4), xlim = c(0.1, 5), col="orange", add=TRUE) curve(dexp(x, rate=1/5), xlim = c(0, 5), col="yellow", add=TRUE) curve(dexp(x, rate=1/6), xlim = c(0, 5), col="yellow", add=TRUE) curve(dexp(x, rate=1), xlim = c(0, 6), col="red", add=TRUE)
Breakdown of the Code:
ggplot
Part: This section creates a bar plot usingggplot2
with labels and a custom color scale. It also adds frequency labels on the bars.- Exponential Curves: The base plot section generates a series of exponential decay curves with different rate parameters (
rate = 3, 2, 1, 1/2, 1/3, ...
), plotting them in various colors on the same graph.
Would you like further clarification on any specific part of the code?
Here are 5 follow-up questions related to this:
- How does
geom_bar()
function work in R? - What is the purpose of using
geom_text()
in the bar plot? - How does the
dexp()
function relate to the exponential distribution? - Why are multiple exponential curves plotted with different rates?
- What effect does
add=TRUE
have when plotting curves?
Tip: Using different color schemes helps in distinguishing between different datasets or models in the same plot.
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Math Problem Analysis
Mathematical Concepts
Data Visualization
Exponential Distribution
Curve Fitting
Formulas
Exponential decay formula: f(x) = 位e^(-位x)
R ggplot2 geom_bar() for bar plots
dexp() function for exponential distribution
Theorems
Exponential Distribution Theorem
Suitable Grade Level
Grades 10-12 (Advanced High School) / Undergraduate