First — talk for 2 minIs anyone's parent or guardian in a union? A friend's parent? A neighbor? If no one, Mr. Bennett will share briefly about the teachers' union.
Why do unions matter?
For most of its history, Samsung did not allow workers to form a union. Workers who tried to organize were often fired or pressured to quit. So when Samsung made huge profits, workers had no real way to push for a fair share.
In 2020, after government pressure and a corruption scandal, Samsung apologized and ended its no-union policy. Workers slowly built up the National Samsung Electronics Union. By 2024 it had over 30,000 members. The union pushed Samsung to share profits during the AI memory boom — and won a deal: about 10% of profits as worker bonuses. But Samsung kept the bonuses capped at 50% of a worker's base salary, so no matter how big the company's profits got, each bonus could not grow past that fixed limit.
At rival SK Hynix, the union saw what Samsung's workers had won. They asked for the same 10% — but with no cap. SK Hynix agreed in September 2024. Union wins build on each other — each contract sets a new floor for the next. SK Hynix's workers won more — but just how much of a difference do you think that actually makes?
Problem\(P(t)\) is Samsung chip-division operating profit (USD billions), \(t\) = years since 2024. Find an equation defining \(P(t)\).
DataSamsung chip-division profit was about \$17 billion in 2024 and is projected at about \$153 billion for 2026 (Q1 2026 alone hit \$38B in chip profit). Use the form \(P(t) = a \cdot b^{t}\).
Word Bank
starting value
isolate
substitution
exponent
equation
simplify
Number Bank
17
3
9
153
27
| # | Reasoning (fill in) | Math |
|---|
| 1 |
Identify \(a\). It is the value when \(t = 0\). The math name is . |
\(a = \) |
| 2 |
Plug the second point in: at \(t = 2\), the profit is 153. We call this swap . |
\(153 = 17 \cdot b^{2}\) |
| 3 |
Divide both sides by 17 to \(b^{2}\). |
\(b^{2} = \dfrac{153}{17} = 9\) |
| 4 |
Take the square root of both sides to find \(b\). |
\(b = \sqrt{9} = \) |
| 5 |
Write the equation using \(a\), \(b\), and \(t\). |
\(P(t) = 17 \cdot 3^{t}\) |
Show your work for Round 1 here
Page 1 of 3 · Unions & the Math of Bonuses · Algebra 2 · Unit 5 · Lesson 6
Problem\(B(t)\) is the average Samsung chip-division worker bonus (thousands of dollars), \(t\) = years since 2024. Write \(B(t)\) and predict the bonus in 2026.
DataIn 2024 the average Samsung worker bonus was about \$40 thousand (capped at 50% of base salary). Per Samsung's capped contract, the bonus grows at a per-year factor of about 1.10. How does this capped rate for workers compare to the company's growth rate you found in problem 1?
Word Bank
growth factor
starting value
substitution
multiply
equation
Number Bank
40
48
2
1.21
44
88
| # | Reasoning (fill in) | Math |
|---|
| 1 |
Identify \(a\), the starting value at \(t = 0\). |
\(a = \) |
| 2 |
The per-year multiplier \(b\) is given, because the cap fixes it. We call this multiplier the . |
\(b = 1.10\) |
| 3 |
Write the equation using \(a\) and \(b\). |
\(B(t) = 40 \cdot 1.10^{t}\) |
| 4 |
To predict 2026, we substitute \(t = 2\) into the equation. |
\(B(2) = 40 \cdot 1.10^{\,\square}\), with \(\square = \) |
| 5 |
Compute \(1.10^{2} = 1.21\), then multiply by 40. |
\(B(2) \approx 40 \cdot 1.21 \approx \$\) K |
Problem
Circle one. The capped worker bonus growth rate of 1.10 is
a lot less·
a little less·
about the same·
greater
than the growth rate of Samsung's company profits.
Your Info Gap answers — fill in from your work with your partner
Round 1 (SK Hynix profit): \(P(t) = \) \(\cdot\) \(t\). The per-year growth factor is about .
Round 2 (SK Hynix bonus): The bonus grows at the same rate as profit (no cap), so \(B(t) = \) \(\cdot\) \(t\).
Predicted 2026 bonus: \(B(2) = \) \(\cdot\) 2 \(\approx\) \$ thousand. (~× bigger than 2024.)
Conclude
Which union would you want to be in — Samsung or SK Hynix?
Samsung's union is planning a strike demanding their bonuses match SK Hynix's no-cap deal. Samsung's workers won 10% profit-share first, but kept the cap. SK Hynix's union learned from that and won 10% with no cap.
Do the math: Compare profit kept by each company after paying workers. Samsung's numbers are given. Use your Round 1 and Round 2 work to fill in SK Hynix's.
Samsung — given (2026)
Profit: ~\$153B
Total bonuses: ~\$1.4B (capped at salary)
Company kept: \$153B − \$1.4B \(\approx\) \$151.6B
SK Hynix — compute (2026)
Profit \(P(2) = 17 \cdot b^{2}\), with \(b^{2} \approx 9.94\): B
Total bonuses = \$ K × 35{,}000 \(\approx\) \$ B
Company kept: − \(\approx\) \$ B
Reflect: Both companies kept billions. Whose deal seems more fair? Which union would you join — and why?
Page 2 of 3 · Unions & the Math of Bonuses · Algebra 2 · Unit 5 · Lesson 6
Tier 2 · General Academic Words
- agreement — a deal between two or more groups about how something will work.
- average — the typical amount when you spread numbers evenly across all the workers.
- cap — a top limit on how high something can go.
- contract — a written agreement that says exactly what each side promises to do.
- estimate — a careful guess based on what you know.
- factor — the number you multiply by (like the per-year growth factor of 1.10).
- predict — to say in advance what is likely to happen, using a pattern.
- profit — the money a company has left after paying all of its costs.
- projected — what experts expect a number to be in the future, based on a pattern.
- record — bigger than ever before; a new high.
- rival — a company or person that competes for the same customers or workers.
- scrapped — got rid of; threw out.
- threatened — said they would do something serious unless things changed.
Tier 3 · Chip, Union, & Math Words
- microchip — a tiny computer part, smaller than your fingernail, that does math and stores information inside phones, cars, and AI servers.
- chip-division — the part of a company that builds microchips (Samsung calls theirs “DS”; SK Hynix is mostly all chips).
- HBM (High Bandwidth Memory) — a stack of fast memory chips used to feed AI processors.
- AI memory boom — the period (around 2023–2026) when AI companies bought so much HBM that chip-maker profits exploded.
- operating profit — the money a company earns from its main business (selling chips), before taxes and interest.
- profit-share — a deal where a company pays workers a bonus equal to a percent of company profits.
- no-cap clause — a line in a contract that removes any upper limit on how big the bonus can grow.
- bonus — extra pay on top of a worker’s regular salary.
- base salary — the regular yearly pay a worker earns, not counting bonuses.
- union — a group of workers who join together to bargain with their employer for better pay and conditions.
- strike — when union workers stop working until the company agrees to better terms.
- per-year factor (b) — the number you multiply by each year for one-year exponential growth.
- starting value (a) — the amount at year 0, before any growth has happened.
- y-intercept — the point where a graph crosses the y-axis (when x = 0). It equals the starting value.
- exponential growth — growth that multiplies by the same factor over equal time intervals.
- square root — the number you multiply by itself to get a given value (\(\sqrt{9} = 3\) because \(3 \cdot 3 = 9\)).
Page 3 of 3 · Unions & the Math of Bonuses · Algebra 2 · Unit 5 · Lesson 6