Exponential Growth & Logarithms | SAT Math Shortcuts
🔥 SAT MATH 2027
Exponential Growth & Logarithms
Master the Formulas. Understand the Patterns. Score Higher.
🎯 TARGET: 800
3
Core Topics
4
Log Rules
5+
Real Examples
📥 Complete SAT Math Guide
⬇️ Full PDF with formulas + practice questions
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Exponential growth and logarithms are tested on almost every SAT Math section. Master these 3 core topics with formulas, examples, and real-life applications.
📈 1. Exponential Growth
Exponential Growth Formula HIGH YIELD
A = P(1 + r)^t
A = final amount
P = initial amount
r = growth rate (in decimal)
t = time (in years)
P = initial amount
r = growth rate (in decimal)
t = time (in years)
💡 Real Life Example: If $100 is invested at 5% annual growth for 10 years:
A = 100(1.05)^10 = $162.89
A = 100(1.05)^10 = $162.89
💰 2. Compound Interest
Compound Interest Formula HIGH YIELD
A = P(1 + r/n)^(nt)
A = final amount
P = principal (initial amount)
r = annual interest rate (in decimal)
n = number of times compounded per year
t = time in years
P = principal (initial amount)
r = annual interest rate (in decimal)
n = number of times compounded per year
t = time in years
💡 Real Life Example: You invest $500 at 6% APR, compounded monthly (n=12) for 5 years:
A = 500(1 + 0.06/12)^(12×5) = $674.43
A = 500(1 + 0.06/12)^(12×5) = $674.43
🔢 3. Log Properties (Basic)
Product Rule ESSENTIAL
logb(MN) = logbM + logbN
Quotient Rule ESSENTIAL
logb(M/N) = logbM - logbN
Power Rule ESSENTIAL
logb(M^k) = k × logbM
Basic Rules
logbb = 1
logb1 = 0
🌍 Where You See Exponential Growth & Logs!
👥 Population Growth
💰 Savings & Investments
🏠 Loan & Mortgage Calculations
🦠 Bacteria / Virus Growth
📉 Radioactive Decay
📊 Data Science & ML
📊 SAT Math Topic Breakdown
| Topic | % of Test | Approx. Questions |
|---|---|---|
| Exponential Functions | 10-15% | 4-6 |
| Compound Interest | 5-8% | 2-3 |
| Logarithms | 5-8% | 2-3 |
| Linear vs Exponential | 5-10% | 2-4 |
| Non-Linear Functions | 15-20% | 6-8 |
🧠 Pro Tips for SAT Math Success
💡 Always Identify P, r, n, t First: For compound interest questions, write down what each variable is before plugging into the formula.
💡 Know When to Use Logs: If you need to solve for an exponent, use logs. Example: 2^x = 16 → x = log₂16 = 4.
💡 Watch for Half-Life & Decay: Decay uses the same formula but with (1 - r) instead of (1 + r).
💡 Don't Use the Wrong Base: Logb means base b. Common bases are 10 and e (natural log).
💡 Use the Calculator Wisely: For logs, use the change of base formula: logba = log a / log b.
💡 Practice Word Problems: SAT loves word problems. Practice translating words into exponential formulas.
❌ Common Mistakes to Avoid
- ❌ Forgetting to convert percentages to decimals (5% → 0.05)
- ❌ Using the wrong base for logarithms
- ❌ Confusing growth (1+r) with decay (1-r)
- ❌ Forgetting about compounding frequency (n)
- ❌ Misreading the question — "quarterly" means n=4
- ❌ Not checking if the answer makes sense logically
❓ Frequently Asked Questions
How often are exponential functions tested on SAT?
Almost every SAT Math section has at least 3-4 questions on exponential functions, growth, and decay.
Do I need to memorize log properties?
Yes. Product, Quotient, and Power Rules are tested frequently. Memorize them.
What's the difference between linear and exponential growth?
Linear: grows by same amount each time. Exponential: grows by same percentage each time — it accelerates.
What's the most common mistake on compound interest?
Forgetting to divide r by n. Always do r/n first, then add 1, then raise to (n×t).
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