Exponents, Roots, and Logarithms

/**
 * Fintech Math Bootcamp · Lesson 005 of 120
 * Exponents, Roots, and Logarithms
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: Finding the growth factor and the time it takes
 * Rule:     100 × 1.05³ = 115.7625
 *
 * Try it:   Does the cube root return 5% or 1.05?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson005() {
  const start = 100, factor = 1.05, periods = 3;
  const future = start * factor ** periods;
  const root = (future / start) ** (1 / periods);
  const doublingPeriods = Math.log(2) / Math.log(factor);
  const result = {future, root, doublingPeriods};
  return result;
}

export const checkedResult = {"future":115.76250000000002,"root":1.05,"doublingPeriods":14.206699082890461};

// Run this file directly: npx tsx lessons/01-mathematical-language-and-quantitative-reasoning/005-exponents-roots-and-logarithms.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson005(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 005 of 120
Exponents, Roots, and Logarithms
Module 01: Mathematical Language and Quantitative Reasoning

Scenario: Finding the growth factor and the time it takes
Rule:     100 × 1.05³ = 115.7625

Try it:   Does the cube root return 5% or 1.05?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json
import math


def lesson005() -> dict:
    start, factor, periods = 100, 1.05, 3
    future = start * factor**periods
    root = (future / start) ** (1 / periods)
    doubling_periods = math.log(2) / math.log(factor)
    result = {"future": future, "root": root, "doublingPeriods": doubling_periods}
    return result


if __name__ == "__main__":
    print(json.dumps(lesson005(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 005 of 120
 * Exponents, Roots, and Logarithms
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: Finding the growth factor and the time it takes
 * Rule:     100 × 1.05³ = 115.7625
 *
 * Try it:   Does the cube root return 5% or 1.05?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

public class Main {
    static final class GrowthFacts {
        final double future;
        final double root;
        final double doublingPeriods;

        GrowthFacts(double future, double root, double doublingPeriods) {
            this.future = future;
            this.root = root;
            this.doublingPeriods = doublingPeriods;
        }
    }

    static GrowthFacts lesson005() {
        double start = 100, factor = 1.05, periods = 3;
        double future = start * Math.pow(factor, periods);
        double root = Math.pow(future / start, 1 / periods);
        double doublingPeriods = Math.log(2) / Math.log(factor);
        GrowthFacts result = new GrowthFacts(future, root, doublingPeriods);
        return result;
    }

    public static void main(String[] args) {
        GrowthFacts result = lesson005();
        System.out.println(object(
            "future", num(result.future),
            "root", num(result.root),
            "doublingPeriods", num(result.doublingPeriods)));
    }

    // Formats a double the way JSON.stringify does: whole numbers without ".0", null for NaN or infinity.
    static String num(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return String.valueOf((long) x);
        return String.valueOf(x);
    }

    static String quote(String text) {
        return "\"" + text.replace("\\", "\\\\").replace("\"", "\\\"") + "\"";
    }

    // Indents an already formatted JSON value by one level.
    static String nested(String json) {
        return json.replace("\n", "\n  ");
    }

    static String object(String... keysAndValues) {
        if (keysAndValues.length == 0) return "{}";
        StringBuilder out = new StringBuilder("{");
        for (int i = 0; i < keysAndValues.length; i += 2) {
            out.append(i == 0 ? "\n  " : ",\n  ")
               .append(quote(keysAndValues[i])).append(": ").append(nested(keysAndValues[i + 1]));
        }
        return out.append("\n}").toString();
    }
}

// Fintech Math Bootcamp · Lesson 005 of 120
// Exponents, Roots, and Logarithms
// Module 01: Mathematical Language and Quantitative Reasoning
//
// Scenario: Finding the growth factor and the time it takes
// Rule:     100 × 1.05³ = 115.7625
//
// Try it:   Does the cube root return 5% or 1.05?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run it: go run main.go

package main

import (
	"encoding/json"
	"fmt"
	"math"
)

type GrowthFacts struct {
	Future          float64 `json:"future"`
	Root            float64 `json:"root"`
	DoublingPeriods float64 `json:"doublingPeriods"`
}

func lesson005() GrowthFacts {
	start, factor, periods := 100.0, 1.05, 3.0
	future := start * math.Pow(factor, periods)
	root := math.Pow(future/start, 1/periods)
	doublingPeriods := math.Log(2) / math.Log(factor)
	result := GrowthFacts{Future: future, Root: root, DoublingPeriods: doublingPeriods}
	return result
}

func main() {
	printJSON(lesson005())
}

// printJSON prints a value as JSON indented with two spaces, like JSON.stringify(value, null, 2).
func printJSON(value any) {
	out, err := json.MarshalIndent(value, "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 005 of 120
 * Exponents, Roots, and Logarithms
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: Finding the growth factor and the time it takes
 * Rule:     100 × 1.05³ = 115.7625
 *
 * Try it:   Does the cube root return 5% or 1.05?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: g++ -std=c++17 -o main main.cpp && ./main
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// Formats a double the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
std::string num(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    auto [end, error] = std::to_chars(buffer, buffer + sizeof buffer, x);
    (void)error;
    return std::string(buffer, end);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') out += '\\';
        out += c;
    }
    return out + "\"";
}

// Indents an already formatted JSON value by one level.
std::string nested(const std::string& json) {
    std::string out;
    for (char c : json) {
        out += c;
        if (c == '\n') out += "  ";
    }
    return out;
}

std::string object(const std::vector<std::pair<std::string, std::string>>& fields) {
    if (fields.empty()) return "{}";
    std::string out = "{";
    for (std::size_t i = 0; i < fields.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += quote(fields[i].first) + ": " + nested(fields[i].second);
    }
    return out + "\n}";
}

struct GrowthFacts {
    double future;
    double root;
    double doublingPeriods;
};

GrowthFacts lesson005() {
    const double start = 100, factor = 1.05, periods = 3;
    const double future = start * std::pow(factor, periods);
    const double root = std::pow(future / start, 1 / periods);
    const double doublingPeriods = std::log(2.0) / std::log(factor);
    const GrowthFacts result{future, root, doublingPeriods};
    return result;
}

int main() {
    const GrowthFacts result = lesson005();
    std::cout << object({
        {"future", num(result.future)},
        {"root", num(result.root)},
        {"doublingPeriods", num(result.doublingPeriods)}
    }) << "\n";
}

//! Fintech Math Bootcamp · Lesson 005 of 120
//! Exponents, Roots, and Logarithms
//! Module 01: Mathematical Language and Quantitative Reasoning
//!
//! Scenario: Finding the growth factor and the time it takes
//! Rule:     100 × 1.05³ = 115.7625
//!
//! Try it:   Does the cube root return 5% or 1.05?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct GrowthFacts {
    future: f64,
    root: f64,
    doubling_periods: f64,
}

fn lesson005() -> GrowthFacts {
    let (start, factor, periods): (f64, f64, f64) = (100.0, 1.05, 3.0);
    let future = start * factor.powf(periods);
    let root = (future / start).powf(1.0 / periods);
    let doubling_periods = 2.0_f64.ln() / factor.ln();
    let result = GrowthFacts { future, root, doubling_periods };
    result
}

fn main() {
    let result = lesson005();
    println!(
        "{}",
        object(&[
            ("future", num(result.future)),
            ("root", num(result.root)),
            ("doublingPeriods", num(result.doubling_periods)),
        ])
    );
}

/// Formats a number the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
fn num(x: f64) -> String {
    if x.is_finite() {
        format!("{}", x)
    } else {
        "null".to_string()
    }
}

fn quote(text: &str) -> String {
    format!("\"{}\"", text.replace('\\', "\\\\").replace('"', "\\\""))
}

/// Indents an already formatted JSON value by one level.
fn nested(json: &str) -> String {
    json.replace('\n', "\n  ")
}

fn object(fields: &[(&str, String)]) -> String {
    if fields.is_empty() {
        return "{}".to_string();
    }
    let lines: Vec<String> = fields
        .iter()
        .map(|(key, value)| format!("  {}: {}", quote(key), nested(value)))
        .collect();
    format!("{{\n{}\n}}", lines.join(",\n"))
}

/**
 * Fintech Math Bootcamp · Lesson 005 of 120
 * Exponents, Roots, and Logarithms
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: Finding the growth factor and the time it takes
 * Rule:     100 × 1.05³ = 115.7625
 *
 * Try it:   Does the cube root return 5% or 1.05?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/exponents-roots-and-logarithms/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: dotnet run  (inside a console project that holds this Program.cs)
 */

using System.Text.Json;

var jsonOptions = new JsonSerializerOptions { WriteIndented = true, PropertyNamingPolicy = JsonNamingPolicy.CamelCase };
Console.WriteLine(JsonSerializer.Serialize(Lesson005(), jsonOptions));

static GrowthFacts Lesson005()
{
    double start = 100, factor = 1.05, periods = 3;
    var future = start * Math.Pow(factor, periods);
    var root = Math.Pow(future / start, 1 / periods);
    var doublingPeriods = Math.Log(2) / Math.Log(factor);
    var result = new GrowthFacts(future, root, doublingPeriods);
    return result;
}

record GrowthFacts(double Future, double Root, double DoublingPeriods);