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Exponential and Logarithmic Functions

Fifteen topics on multiplicative change and how to undo it. Arithmetic and geometric sequences, exponential functions built on a constant factor, composition and inverse functions, the logarithm as the exponent question, log properties and equation solving with domain discipline, data modeling with exponentials and logs, and reading semi-log plots.

Topics
Key forms For every problem in this unit
Arithmetic sequence
an = a0 + d·n (constant difference d)
Geometric sequence
gn = g0 · rn (constant ratio r)
Exponential function
f(x) = a · bx, a = initial value, b = growth factor
Factor vs rate
b = 1 + r (5% growth → b = 1.05; 5% decay → b = 0.95)
Log means exponent
logb(c) = a ⇔ ba = c
Product rule
logb(xy) = logbx + logby
Power rule
logb(xk) = k·logbx
Inverse pair
f(f−1(x)) = x on the appropriate domain; graphs reflect over y = x
No rule exists for
logb(x + y) — it does not split
Unit 2 tools
Challenge bank
1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

0 mastered · 0 to revisit · 60 total
Question
Tap card to reveal explanation
Worked solution
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Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 15 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

20questions
15topics
14codes covered
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Course so far

Check what stuck.

Units 1 through 2, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 40-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 40questions
29topics
28codes covered
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