Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 13 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 8 — Analyze and apply exponential and logarithmic functions and equations, including growth/decay models and compound interest.

This file holds two pieces: (A) the Module 13 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 13 meeting Tue Nov 24 and — note: Thanksgiving break (Thu Nov 26 – Fri Nov 27) means there is no Thursday session this week. End-of-week work is still due Sun Nov 29, 11:59 p.m. Adjust times to match your section.

(A) Module 13 Overview — Start Here

Welcome to Week 13: Exponential Functions

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

This week we cross into new territory. Every function you've studied so far has had the variable in the base. Exponential functions flip that: the variable is the exponent. That one shift produces the curves of compound interest, population growth, radioactive decay, and viral spread — and understanding them starts right here.

Short week notice: Thanksgiving break falls Thursday–Friday (Nov 26–27), so we only meet Tuesday this week. Plan ahead: the quiz, discussion, and assignment all close Sunday Nov 29. Start early — you have one fewer in-class session and a holiday in the middle.

The week's big question

"What happens when the variable moves to the exponent — and how does that one change produce growth, decay, compound interest, and the natural base e?"

By Sunday you'll evaluate an exponential expression at any input (including negative ones), read a graph to name the y-intercept and horizontal asymptote, tell growth from decay just by looking at the base, and apply the compound-interest formulas to a real money problem.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Evaluate an exponential function f(x) = a·bˣ at any x-value and classify it as growth or decay by looking at b.
• [ ] Read the graph of an exponential function — locate the y-intercept (0, a), state the horizontal asymptote y = 0, and say whether the function is increasing or decreasing.
• [ ] Recognize the natural base e (≈ 2.718) and use the formula A = Peʳᵗ for continuous compounding alongside A = P(1 + r/n)^(nt) for periodic compounding.
• [ ] Set up and evaluate a growth or decay model (population growth, depreciation, or compound interest) and interpret the answer in context.

What's due this week, and when

Work these in order — each one gets you ready for the next. Short week: only one class session Tuesday Nov 24. Start the readings and tutorial early.

Heads-up on the Thanksgiving timing: your initial discussion post is technically due Friday Nov 27 — that's the holiday itself. Post it Wednesday or Thursday morning to stay comfortable, or plan to post on Friday if you're at a table with WiFi. Replies close Sunday as usual.

Late policy reminder: 10% off per day late. If Thanksgiving travel creates a problem, reach out before the deadline.

How to succeed this week

• Base is everything. Before any calculation, identify a and b. If b > 1, the function grows. If 0 < b < 1, it decays. The base tells you the whole story.
• The y-intercept is always (0, a). Plug in x = 0 and you get a·b⁰ = a·1 = a, every time. Don't compute it; just read the a.
• The asymptote is always y = 0. Exponential functions never touch the x-axis; they glide toward it but never reach it.
• Don't confuse the exponent rules. f(x) = 2ˣ is exponential — variable in the exponent. g(x) = x² is a polynomial — variable in the base. They look related but behave completely differently.
• Memorize the two interest formulas and what every letter means. A = P(1 + r/n)^(nt) and A = Peʳᵗ. Label each piece before you plug in a single number.
• Use Desmos to check your graphs. Type 3*2^x and look at the y-intercept and the behavior as x goes left. Confirm it matches your algebra.

One session, one break, and five days to Sunday. You've got this.

(B) Welcome Announcement — Module 13

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Nov 23, 2026 (so students see it before Tuesday's session). If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Nov 23."

Subject: Week 13 — Exponential Functions (short week — plan ahead!) 📈

Hi everyone,

Quick Thanksgiving heads-up before we dive in: we only meet once this week (Tuesday Nov 24 — no class Thursday or Friday). Everything still closes Sunday Nov 29, so start early and give yourself breathing room.

Now the fun part. Every function we've studied has had the variable in the base: x², x³, √x. This week we flip it — the variable goes into the exponent, and that one change produces some of the most important curves in science, economics, and everyday life. Compound interest? Exponential. Population growth? Exponential. Viral spread, radioactive decay, drug metabolism? All exponential. You've been living inside these curves for years; this week you finally understand them.

The week's big question: What happens when the variable moves to the exponent?

Three things not to miss:

1. Lecture Tutorial 13 — take your approved chatbot through exponential functions, growth vs. decay, graph features, and the natural base e. Submit the share link. Due Sun Nov 29.
2. Quiz 13 (no AI) and Discussion 13 — "Exponential in the Wild" both close Sun Nov 29. The discussion asks where you see exponential growth or decay in your own field or life — it's genuinely interesting. Post your initial summary by Friday (the holiday — plan ahead) and reply to two classmates by Sunday.
3. Assignment 13 — four AI-coached problems on evaluating, graphing, and compound interest. Due Sun Nov 29.

One warning to file away: don't mix up the exponent rules from Week 1 with exponential functions. When we write 2ˣ, the x is in the exponent and the 2 is fixed — that's completely different from x², where x is the base. They look similar but behave in opposite ways. We'll unpack exactly why on Tuesday.

Open the Start Here / Module Overview page for the full due-date table. See you Tuesday — and enjoy Thanksgiving.

Prof. Calloway