Exponential Growth Models
I can write an exponential growth model and read its rate and starting value.
The problem this sheet solves
Students do the one conversion they were taught, turning 5% into 0.05, and drop it straight into the base. The 1 is what keeps what you already had; the r is only the increase. The model then contradicts the word GROWTH in its own problem, and students hand it in because nothing told them the answer should be checked against the story. This sheet makes the base 1 + r explicit and then TESTS the wrong model at t = 1, where 600 becoming 30 needs no explanation. It also runs the skill backwards, recovering a rate from a given factor, which is where students discover that 1.08 does not mean 8 percent of anything until it is read properly.
The key rule
The base is 1 + r, never r. The 1 keeps what you already had; the r adds the increase. A base below 1 shrinks, so 0.05 is not growth of any kind.
5% means 1.05, not 0.05.
Watch out
The mistake: For 5% growth on 600 a student writes y = 600 · (0.05)t.
The fix: y = 600 · (1.05)t. Test the wrong one at t = 1: 600 · 0.05 = 30, so a town of 600 has become 30. The problem said growth, so the model has to grow.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.