Week 13 — Readings & Resources

Your primary reading is Chapter 13 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 67–84 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (19–21 min total)

• How does compound interest work? — Consumer Financial Protection Bureau
• Ex: Exponential Functions: Growth Rate and Growth Factor — Mathispower4u
• How To Graph Exponential Functions — The Organic Chemistry Tutor

① Is it growing or shrinking? Growth factors, decay, and half-life

Chapter 13, Section “Use the base to tell growth from decay” · Session 1, Segment 4, “Growth and decay” · Remember: the base decides, so a base above 1 means growth and a base between 0 and 1 means decay.

• Ex: Exponential Functions: Growth Rate and Growth Factor — Mathispower4u — short examples that turn a percent rate into a growth factor and back, and read the initial value from the formula. This builds on Week 1's work with the exponent rules. (video, 5 min) (captions: creator)
• Ex: Determine Exponential Decay Functions Given Decay Rate and Initial Value — Mathispower4u — the decay side of the same move: a starting amount and a percent loss become a formula with a factor between 0 and 1. (video, 4 min) (captions: creator)
• Radioactive Decay — US Environmental Protection Agency — a short science page that defines half-life as the time for half of a radioactive sample to decay; read the half-life paragraph and connect it to the halving sample, and use it while working through the Week-13 module overview. (reading, 3–5 min)

② What does the graph look like? Intercept, asymptote, and shape

Chapter 13, Section “Read the graph from the formula” · Session 1, Segment 5, “Reading the graph” · Remember: the curve crosses the y-axis at the initial value and hugs the x-axis without ever touching it.

• How To Graph Exponential Functions — The Organic Chemistry Tutor — builds a table of values, plots the points, and reads the horizontal asymptote, domain, and range; pause before each table and fill it in yourself. (video, 11 min) (captions: automatic)
• Quick Review on Graphing Exponential Functions — Brian McLogan — a compact review of the starting graph of an exponential, where it crosses the y-axis, and why it never reaches the x-axis. (video, 8 min) (captions: automatic)

③ How does money grow? Compound interest

Chapter 13, Section “Compare compound and simple interest” · Session 2, Segment 7, “Compound interest” · Remember: compound interest multiplies the balance each period, so later interest is earned on earlier interest.

• How does compound interest work? — Consumer Financial Protection Bureau — a one-screen government explainer that works two years of yearly compounding step by step, the same way the chapter does, with its own numbers. (reading, 3–5 min)
• Compound Interest Calculator — Investor.gov — a free calculator from the US Securities and Exchange Commission; enter a starting amount, a rate, and a compounding frequency, and compare annual with twice-a-year compounding to check your own hand work. (reading, 5–10 min)
• Compound Interest - More than Once Per Year — Patrick J — works the formula with more than one compounding period a year, showing where the rate per period and the number of periods come from. (video, 7 min) (captions: automatic)

④ Where does e come from? Continuous compounding

Chapter 13, Section “Find the natural base e and compound continuously” · Session 2, Segment 8, “The natural base e” · Remember: compounding more and more often levels off at the fixed number e, about 2.71828.

• An Intuitive Guide To Exponential Functions & e — BetterExplained — a plain-language essay on why compounding more and more often levels off at e instead of growing without end; read the parts on growth and compounding and skip the later sections on logarithms. (reading, 12–18 min)
• Interest Compounded Continuously — The Organic Chemistry Tutor — worked examples of the continuous-compounding formula on a calculator, using the e key. Stop here before logarithms; next week takes that up. (video, 6 min) (captions: automatic)

Optional one-stop reference (free online reference)

• e — Wolfram MathWorld — a mathematics encyclopedia's entry on the constant e; read the opening lines with its decimal value and the note that e is irrational, and skip the limits, series, and continued fractions that follow, which go beyond this course. (reading, 3–5 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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