First — talk for 2 minHas anyone heard about a strike — UAW, teachers, baristas, anyone? What did the workers want? What happened during the strike? If no one, Mr. Bennett will share about the 2023 UAW strike.
How long does $825 million of leverage last?
A union strike works when the workers can outlast the company. Workers stop making cars; the company stops making profit. Whoever can hold out longer wins the contract. The number that decides who wins is not on a picket sign — it is in a bank account called the strike fund.
In September 2023, the United Auto Workers (UAW) walked out on Ford, GM, and Stellantis with about $825 million in their strike fund. The union has about 146,000 members at the Big 3, and strike pay is $500 per worker per week. If every member walked out at once, the fund would burn at \(146{,}000 \times \$500 = \$73\) million every single week.
Instead of calling a full strike, UAW tried something new: a Stand-Up Strike, where only some plants walked out at a time. Fewer strikers means a slower burn. But the fund also earns interest and grows from public donations, while a longer strike makes more plants want to join — so the real burn rate is not flat. The fund value \(F(t)\) follows the equation \(F_0 \cdot b^{t} = k\), and the question becomes: at what week \(t\) does the fund hit the floor?
Worked Example #1 — Full strike (linear burn): how many weeks does $825M last?
ProblemIf every UAW member at the Big 3 walks out at once, the fund \(F(t)\) (in millions of dollars) drops by a fixed amount each week. Solve for the number of weeks \(t\) until the fund is empty.
DataFund: \$825 million. Members on strike: 146,000. Strike pay: \$500 / worker / week. Weekly burn = \(146{,}000 \times \$500 = \$73\)M / week. Equation: \(73t = 825\).
Word Bank
divide
multiply
burn rate
subtract
isolate
weeks
linear
Number Bank
73
11.30
825
500
8.25
146
| # | Reasoning (fill in) | Math |
|---|
| 1 |
Each week, $73M leaves the fund. This is the weekly . |
\(73t = 825\) |
| 2 |
To \(t\), undo the multiplication by 73. |
\(t = \dfrac{825}{73}\) |
| 3 |
825 by 73 on a calculator. |
\(t = \dfrac{\,\,\text{}\,\,}{\,\,\text{}\,\,} \approx \) |
| 4 |
This is a equation — \(t\) is not in an exponent, so no log is needed. |
No log used. |
| 5 |
Answer in : at full strike, the fund lasts about 11.30 weeks (≈ 2.6 months). |
\(t \approx 11.30\) weeks |
Page 1 of 3 · UAW Strike Fund Math · Algebra 2 · Unit 5 · Lesson 14
Worked Example #2 — Exponential burn: when does the fund hit $100M?
ProblemThe fund burns 9% of its balance each week (more plants join the strike, harder to feed every worker, but donations slow the loss to a fixed percentage). Solve for the number of weeks \(t\) until the fund hits \$100M.
DataStarting fund \(F_0 = 825\). Per-week factor \(b = 0.91\) (keeps 91% each week). Target \(k = 100\). Equation: \(825 \cdot (0.91)^{t} = 100\). Solve for \(t\) using \(\log_b(x)\).
Word Bank
isolate
logarithm
inverse
divide
exponent
decay factor
add
Number Bank
0.91
100
825
0.1212
22.4
7.25
−0.0410
−0.9172
| # | Reasoning (fill in) | Math |
|---|
| 1 |
Start with the equation. The variable \(t\) is locked inside the . |
\(825 \cdot (0.91)^{t} = 100\) |
| 2 |
both sides by 825 to isolate \((0.91)^{t}\). |
\((0.91)^{t} = \dfrac{\,\,\text{}\,\,}{\,\,\text{}\,\,} \approx 0.1212\) |
| 3 |
Apply the — the inverse of an exponential. Use base 0.91 here, so \(t = \log_b(k/F_0)\). |
\(t = \log_{0.91}(0.1212)\) |
| 4 |
Use the change-of-base rule to compute on a calculator. 0.91 is the . |
\(t = \dfrac{\log(0.1212)}{\log(0.91)}\) |
| 5 |
Compute. The answer in weeks is about . |
\(t \approx \dfrac{-0.9172}{-0.0410} \approx \) wk |
Activity 2 · The Leverage Clock — Scenarios A/B/C
Scenario A · Full strike (146k workers): burn = \$M / week. Solve \(73t = 825\). \(t \approx\) weeks.
Scenario B · Stand-Up Strike (46k workers at peak): burn = 46{,}000 \(\times\) \$500 = \$M / week. Solve \(23t = 825\). \(t \approx\) weeks.
Scenario C · Exponential burn (9% / week loss): Solve \(825 \cdot (0.91)^{t} = 100\). \(t = \dfrac{\log(\,\,\text{}\,\,/\,\,\text{}\,\,)}{\log(\,\,\text{}\,\,)} \approx\) weeks.
Conclude
Which strategy gives UAW the most leverage?
UAW's actual 2023 strike lasted 44 days (about 6.3 weeks) and spent only ~$58M of the $825M fund. They settled before any of the three scenarios above ran out. Why? Because leverage is what you don't have to spend — the company saw the burn rate and folded.
Compare the three scenarios. Use your worked examples and your activity answers.
Scenarios A & B — linear
Full strike: \(t = 825/73 \approx\) wk
Stand-Up: \(t = 825/23 \approx\) wk
Leverage gain: Stand-Up lasts about × longer.
Scenario C — exponential decay
\(825 \cdot (0.91)^{t} = 100\): \(t \approx\) wk
Half-life of the fund (when does it hit ~$412M?):
\(t = \log_{0.91}(0.5) \approx\) wk
Reflect: Why does the Stand-Up Strike give workers more weeks of leverage than a full walkout? What other inputs (donations, sectoral bargaining, public solidarity) could a union change to make the fund last even longer?
Page 2 of 3 · UAW Strike Fund Math · Algebra 2 · Unit 5 · Lesson 14
Tier 2 · General Academic Words
- floor — the lowest value something can drop to before something stops working.
- fund — a pile of money saved up to pay for something specific later.
- leverage — the power to push someone to agree to your terms because you can hold out longer than they can.
- member — a person who belongs to a group (like a union).
- outlast — to keep going after something or someone else stops.
- peak — the highest point something reaches.
- scenario — one possible way things could play out.
- target — the value you are aiming for.
Tier 3 · Union, Labor, & Math Words
- UAW (United Auto Workers) — the union that represents workers at Ford, GM, Stellantis, and many other auto plants.
- strike — when union workers stop working until the company agrees to better terms.
- strike fund — money the union saves up so it can pay striking workers while they are not getting a paycheck from the company.
- strike pay — the weekly payment a union sends each striking worker out of the strike fund (UAW = $500/week).
- Stand-Up Strike — UAW's 2023 strategy: only some plants walked out at a time, so the fund burned slower.
- burn rate — how fast the strike fund is being spent each week (members on strike × strike pay).
- contract negotiation — the back-and-forth where the union and the company decide pay, hours, and rules in writing.
- half-life — the time it takes for an amount to drop to half of where it started.
- decay factor — the number you multiply by each time period when something is shrinking (here, \(b = 0.91\) means you keep 91% each week).
- exponential decay — shrinking that multiplies by the same factor each equal time interval (not subtracting a fixed amount).
- logarithm — the inverse of an exponential. Asks "what exponent gives this value?" Written \(\log_b(x)\).
- natural log (ln) — the logarithm with base \(e \approx 2.718\). Used when growth or decay is continuous.
- isolate — to get the variable alone on one side of the equation.
- inverse — an operation that undoes another (log undoes exponential; subtract undoes add).
Page 3 of 3 · UAW Strike Fund Math · Algebra 2 · Unit 5 · Lesson 14