R-Exercise.qmd

---
author: Dr Wei Miao
date: "`r (lubridate::ymd('20240927'))`"
date-format: long
institute: UCL School of Management
title: "Weekly R Exercise"
format: 
  html: default
knitr:
  opts_chunk:
    echo: true
    warning: true
    message: true
    error: true
execute: 
  freeze: auto
  cache: true
editor_options: 
  chunk_output_type: inline
---

# Induction Week

```{r}
#| echo: false
question_index <- 1
```


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### **Question `r question_index<-question_index+1; question_index-1`**
Create a sequence of {1,1,2,2,3,3,3}.

### Answer

```{r}
# solution 1

c(1, 1, 2, 2, 3, 3, 3)

# solution 2

c(rep(1, 2), rep(2, 2), rep(3, 3))

```

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### **Question `r question_index<-question_index+1; question_index-1`**
Create a geometric sequence {2,4,8,16,32} using seq().

### Answer

We can see that the sequence is a geometric sequence with a common ratio of 2.

- The `seq()` function generates a sequence from 1 to 5 with a step of 1.

```{r}

# solution

seq(1, 5, 1) # this generates a sequence from 1 to 5 with a step of 1

```

- The `^` operator calculates the power of 2 raised to the power of the sequence generated by `seq()`. Remember that R is vectorized, so the `^` operator will apply to each element in the sequence.

```{r}

# solution

2^seq(1, 5, 1) # this generates a geometric sequence {2^1, 2^2, 2^3, 2^4, 2^5}

```


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### **Question `r question_index<-question_index+1; question_index-1`**
Create a vector of 10 numbers from 1 to 10, and extract the 2nd, 4th, and 6th elements.

### Answer

```{r}

# solution

x <- 1:10 # create a vector of 10 numbers from 1 to 10

x[c(2, 4, 6)] # use [] to extract the 2nd, 4th, and 6th elements

```

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### **Question `r question_index<-question_index+1; question_index-1`**
Create a vector of 5 numbers from 1 to 5, and check if 3 is in the vector.

### Answer

```{r}

# solution

x <- 1:5 # create a vector of 5 numbers from 1 to 5

3 %in% x # check if 3 is in the vector

```

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### **Question `r question_index<-question_index+1; question_index-1`**
Now the interest rate is 0.1, and you have 1000 pounds in your bank account. Calculate the amount in your bank account after 1 year, 2 years, and 3 years, respectively.

### Answer

First, set the interest rate to 0.1 and the initial amount to 1000.

Then, calculate the amount in your bank account after 1 year, 2 years, and 3 years, respectively.

Since the interest is compounded annually, the formula is:

\[
A = P(1 + r)^n
\]

where:

- \(A\) is the amount in your bank account after \(n\) years
- \(P\) is the initial amount
- \(r\) is the interest rate
- \(n\) is the number of years



```{r}

# solution

interest_rate <- 0.1 # set the interest rate to 0.1

initial_amount <- 1000 # set the initial amount to 1000

# calculate the amount in your bank account after 1 year, 2 years, and 3 years, respectively

# generate the geometric sequence from 1 to 3 years

initial_amount * (1 + interest_rate)^(1:3) # use the formula A = P(1 + r)^n

```

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# Week 1

- The after-class exercise solutions are in the [Week 1 case study](Case-ProfitabilityAnalysis.qmd)