Exponential Functions
Master exponential growth, decay, and compound interest
Practice Problems
Initial: 500, doubles every hour
Initial: $20,000, loses 15% yearly
Pro Tips & Shortcuts
SAT Tip: Exponential functions model real-world growth and decay: population, compound interest, radioactive decay.
SAT Tip: For word problems, identify if the quantity is increasing (growth) or decreasing (decay).
SAT Tip: Convert percentages to decimals: 5% = 0.05. So (1 + r) = 1.05 for 5% growth.
SAT Tip: Doubling means multiply by 2, tripling means multiply by 3, etc.
SAT Tip: Losing 15% means keeping 85%, so multiply by 0.85 (not 0.15!).
The variable is in the exponent - that's what makes it exponential!
If something doubles: b = 2. If it triples: b = 3. If it halves: b = 0.5.
The base (1 + r) is always greater than 1 for growth, less than 1 for decay.
To find the value after n periods, substitute n for x.
For decay, the base is (1 - decay rate). For 15% decay: 1 - 0.15 = 0.85.