Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 15 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 8 — Analyze and apply exponential and logarithmic functions, including solving equations and modeling real-world growth, decay, and financial scenarios.

This file holds two pieces: (A) the Module 15 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 15 meeting Tue Dec 8 and Thu Dec 10, and end-of-week work due Sunday Dec 13, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 15 Overview — Start Here

Welcome to Week 15: Exponential & Logarithmic Equations & Applications

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 is the last full instructional week of the term — and it's the payoff for everything you learned in Weeks 13 and 14. You've seen exponential and logarithmic functions; now we put them to work. Solving "how long until?" is one of the most useful things algebra can do in real life: how long to double your money, how long a drug stays in your system, how long a radioactive substance takes to decay. All of those questions come down to the same tools you build this week.

The week's big question

"If you know the rule for how something grows or shrinks, how do you find out when it hits a target — and how do you make sure your answer is actually valid?"

By Friday you'll solve exponential equations by matching bases and by taking a logarithm of both sides, untangle logarithmic equations by condensing and converting, flag extraneous solutions before they cost you points, and translate a "how long until…" story into algebra and back.

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.

• [ ] Solve exponential equations using the same-base method — rewrite both sides as powers of the same base and set the exponents equal.
• [ ] Solve exponential equations by taking a logarithm of both sides — apply log (or ln) to both sides, pull the exponent down, and isolate the variable.
• [ ] Solve logarithmic equations by condensing to a single log and converting to exponential form — and always check for extraneous solutions (a log argument must be positive).
• [ ] Set up and solve a real-world application — compound interest, doubling time, or half-life — and interpret what the answer means in context.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, then you judge its work. These tools love to skip the domain check on logarithms and accept extraneous solutions — catching that slip is exactly the point.

Late policy reminder: 10% off per day late. Week 16 is finals week — if you're behind, now is the time to talk to me.

How to succeed this week

• Same base first, log second. When you can write both sides with the same base (like 4 and 64 as powers of 4), do it — the answer is cleaner and the work is faster. Only reach for logarithms when the bases don't match.
• Check every logarithmic solution. Sub your answer back in and confirm every log argument is positive. An answer that makes a log argument zero or negative is extraneous — cross it out, don't just flag it.
• Write the application equation before you solve it. For compound interest, doubling time, and half-life, write out A = Pe^(rt) or A = A₀·b^t with the numbers plugged in, then solve for t. Students who skip straight to algebra lose points for setup.
• Use ln for anything with base e; use log (or log of both sides) for everything else. Pick the one that makes the cancellation obvious.
• The final is next week. This week's exam-prep tutorial for the Week 16 final will cover all of Objective 8 — so this week's problem-solving is also review for the final. Do the work now; your future self will thank you.

You are one week from the finish line. See you Tuesday.

(B) Welcome Announcement — Module 15

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Dec 7, 2026 (module opens Monday; first session Tuesday Dec 8). If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Dec 7."

Subject: Week 15 — the payoff week 🎯

Hi everyone,

One week left before finals — and it's the week where everything from Weeks 13 and 14 comes to life.

This week — Exponential & Logarithmic Equations & Applications — we answer the big question: How do you find the "when" in a growth or decay situation? By Thursday you'll be able to take "how long does it take to double your money at 6% interest?" and solve it — not just estimate, but get the exact algebraic answer. That's a skill worth having long after this course ends.

Three things not to miss:
1. Lecture Tutorial 15 — work through solving exponential and log equations with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. The big habit this week: always check log solutions for negative arguments (the chatbot often forgets). Due Sun Dec 13.
2. Quiz 15 (no AI) and Discussion 15 — "How Long Until…?" also close Sun Dec 13 — the discussion is a short AI dialogue about a real-world model you pick; start early and leave time for two peer replies.
3. Assignment 15 — four problems covering every technique from this week; AI-coached and self-scored. Due Sun Dec 13.

One heads-up: Week 16 is your final exam and its prep bundle. This week's work is also excellent review for that — the applications we solve Tuesday and Thursday will appear in the final's study guide. Do the problems yourself before the exam; the chatbot can help you understand, but the quiz and final are pen-and-paper.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates.

See you Tuesday,
Prof. Calloway