Algebra II Lesson

Zombie Outbreak: Unlocking Logarithms as the Inverse of Exponential Functions

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10th-11th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.HSF.BF.B.4.A, CCSS.MATH.CONTENT.HSF.LE.A.450 min

Learning Objective

Students will be able to rewrite exponential equations in logarithmic form, evaluate common and natural logarithms, and solve basic exponential equations using logarithms (CCSS.MATH.CONTENT.HSF.BF.B.4.A, CCSS.MATH.CONTENT.HSF.LE.A.4).

Lesson Overview

Students use a zombie virus outbreak context (f(t) = 2^t) to discover that logarithms answer the question 'what exponent do I need?' — progressing from reading exponential equations to evaluating, rewriting, and solving logarithmic expressions.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Erasers or paper towels
Random grouping cards
Four-Quadrant note-taking template (printed or folded paper)

Scaffolded Task Progression

1Task 1

The zombie virus follows f(t) = 2^t. Fill in the table below — find the OUTPUT (number of zombies) for each day.

Day (t)	Zombies f(t) = 2^t
0
1
2
3
4
5

Then SKETCH the graph on your whiteboard.

[ Interactive graph / diagram, available in the full lesson ]

2Task 2

Now flip the question. Instead of 'Given the day, how many zombies?' ask: 'Given the zombies, what day is it?'

Fill in the REVERSE table:

Zombies	Day (t) = ?
1
2
4
8
16
32

In words: you are answering '2 raised to WHAT power gives this number?'

3Task 3

Mathematicians invented a notation for 'the exponent you need.' It's called a LOGARITHM. The rule: 2^t = y ⟺ log₂(y) = t Read log₂(y) as: 'the power of 2 that gives y.' Rewrite each exponential equation in logarithmic form:
a) 2^3 = 8 → log₂(_) = _b) 2^5 = 32 → log₂(_) = _c) 2^0 = 1 → log₂(_) = _d) 2^10 = 1024 → log₂(_) = _

4Task 4

Now go the OTHER direction — convert from logarithmic form back to exponential form. The rule: log_b(y) = x ⟺ b^x = y Rewrite each logarithmic equation as an exponential equation, then EVALUATE:
a) log₂(16) = ? → 2^? = 16 → answer: ___b) log₂(128) = ? → 2^? = 128 → answer: ___c) log₂(1) = ? → 2^? = 1 → answer: ___d) log₂(1/2) = ? → 2^? = 1/2 → answer: ___

5Task 5

The CDC switches to a different tracking system using BASE 10 (common log, written as 'log' with no base shown). Rule: log(x) means log₁₀(x) Evaluate WITHOUT a calculator:
a) log(100) = ___ (Hint: 10^? = 100)b) log(1000) = ___c) log(1) = ___d) log(0.1) = ___ (Hint: 0.1 = 10^?) e) log(10^7) = ___ Bonus: The zombie population is now 10,000. Using f(t) = 10^t, on what day did this happen?

6Task 6

Back to the zombie outbreak! The virus now spreads according to f(t) = 2^t. The CDC needs to SOLVE for the exact day t. Set up and solve each equation by converting to logarithmic form:
a) 2^t = 512 → t = log₂(512) = ___b) 2^t = 4096 → t = ___c) 2^t = √2 → t = ___ (Hint: √2 = 2^?)d) 10^t = 50,000 → t = log(50,000). Use a calculator. Round to 2 decimal places. [ Interactive graph / diagram, available in the full lesson ]

7Task 7

CEILING CHALLENGE — Outbreak Analysis: The zombie population is modeled by P(t) = 3 · 2^t (3 initial zombies, doubling daily).
a) Solve for t when P(t) = 96. Show all algebraic steps.b) A rival virus follows Q(t) = 5^t. On what day does Q(t) = 200? Express your answer as log₅(200), then use the change-of-base formula to evaluate: log₅(200) = log(200) / log(5) Round to 2 decimal places.c) Which virus reaches 1,000 zombies first — P(t) = 3·2^t or Q(t) = 5^t? Solve both and compare. [ Interactive graph / diagram, available in the full lesson ]

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