Advanced Math • 35% of test
Exponential Functions
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Exponential Functions?
Exponential functions model growth and decay—population, compound interest, radioactive decay. The SAT tests recognizing exponential patterns and interpreting parameters in context.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
How do I identify exponential growth vs decay?
If the base b > 1, it's growth. If 0 < b < 1, it's decay. The graph curves up for growth, down for decay.
What's the difference between factor and rate?
Factor is what you multiply by (like 1.1). Rate is the percent change (like 10%). Factor = 1 + rate.
What does the initial value represent?
The starting amount when x = 0. In f(x) = 5·2ˣ, it is 5. Knowing initial values is vital for <a href='/math'>SAT Algebra mastery</a>.
How do I solve for the exponent?
Use logarithms or graph both sides in Desmos and find the intersection.
Is compound interest exponential?
Yes! The more often it compounds, the faster it grows. Practice these models in our <a href='/math/exponential-functions/intermediate'>Intermediate Exponential practice module</a>.
How common are exponential questions?
Expect 2-3 per test. Focus on interpreting parameters in context.
What is the 'Half-Life' formula?
Final = Initial × (0.5)^(t/h), where t is total time and h is the half-life period. The base 0.5 represents decay.
How do I tell if a function is linear or exponential from a table?
In a linear function, the DIFFERENCE between y-values is constant. In an exponential function, the RATIO of y-values is constant.
What does 1.07^t mean in a bank account context?
It represents 7% compound interest per time period t. The 1 represents the initial 100% and 0.07 is the growth.
What if the exponent is negative, like 2^-x?
This is equivalent to (1/2)^x, which represents exponential decay rather than growth, even though the base looks larger than 1.
How do I find the doubling time of a population?
Set the function to twice the initial value (2a = a·bˣ) and solve for x using logarithms or simply graph in Desmos.
What is the 'Horizontal Asymptote' of an exponential function?
For f(x) = a·bˣ, the asymptote is y = 0. The graph gets closer to the x-axis but never touches it (unless vertically shifted).
How do transformations affect exponential graphs?
f(x) + k shifts the asymptote and graph vertically. A multiplier k·f(x) changes the vertical stretch or initial starting value.
Why is the base 'b' never negative in exponential functions?
A negative base would cause the values to oscillate between positive and negative, which doesn't create a smooth continuous curve.
Can I use Desmos to find the growth rate?
Yes! If you have two points, use Desmos regression (y1 ~ a*b^x1) to find the exact base b and initial value a.