Exponential and Logarithmic Functions: Growth, Decay, and Inversion: Math Unit 3, Grade 12 (Letters & Devotion)

Description

Exponential and Logarithmic Functions: Growth, Decay, and Inversion is Unit 3 of Precalculus: Functions, Trigonometry, and Mathematical Modeling (Grade 12), the Letters & Devotion Math course, complete in one printable PDF: 11 lessons, the unit check-up and the answer key, 83 pages.

• Constant ratio vs. constant rate of change in tabular data
• The mechanism connecting percent growth/decay to the exponential function form b^x
• Exponent-rule transformation of exponential growth expressions to reveal an equivalent rate
• The logarithm as the inverse function of an exponential, and why it requires a new function class
• The definition of logarithm and exponential/logarithmic form conversion
• The derivation of log properties from exponent rules
• Solving exponential and logarithmic equations algebraically
• Multi-term exponential/logarithmic equation solving requiring strategic property selection
• E as the limit of (1+1/n)^n and its role in continuous-compounding models
• Model selection among exponential, logarithmic, and polynomial families based on structural data features
• Validity of proposed logarithm properties, tested against the definition of log as inverse exponent

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.