Exponential Functions Test Review

Ace your next math test with this comprehensive exponential functions review from Mario's Math Tutoring! We'll tackle 18 frequently asked questions covering everything from graphing exponential growth and decay functions (including domain, range, asymptotes, and end behavior) to writing exponential equations from given points. Learn how to solve exponential equations by matching bases, identify exponential vs. linear patterns in tables, and apply exponential models to real-world word problems involving classic cars, depreciation, compound interest (monthly and continuously), and bacterial growth. Perfect for students preparing for an exam on exponential functions! Timestamps: 0:00 - Introduction to Exponential Functions Test Review 0:25 - Graphing Exponential Functions: f(x) = 2 * 3^x 0:45 - Exponential Growth vs. Decay & Vertical Stretch 1:00 - Creating a Table for Graphing 1:50 - Identifying Horizontal Asymptotes 2:15 - Y-intercept, Domain, Range, and Asymptote 3:00 - End Behavior (Limits as X approaches Infinity) 3:35 - Graphing Exponential Functions with Transformations: f(x) = -3 * (1/2)^(x-1) + 2 4:00 - Parent Function Table (1/2)^x 4:40 - Applying Reflections, Vertical Stretch, Horizontal & Vertical Shifts 6:00 - Plotting the Transformed Exponential Function 6:20 - Domain, Range, and End Behavior 7:00 - Y-intercept 7:25 - Writing Exponential Equations from Two Points (y = a * b^x) 7:45 - Example 3: Given (0, 5) and (-2, 80) 8:00 - Solving for 'a' using the Y-intercept 8:30 - Solving for 'b' using the second point 9:30 - Example 4: Given (2, -9) and (-1, -36) 10:00 - Setting up a System of Equations 10:45 - Solving for 'a' and 'b' 11:45 - Solving Exponential Equations for X 12:00 - Example 5: (1/2)^x = 8 (Matching Bases) 13:00 - Example 6: (2/3)^x = 16/81 13:25 - Determining if a Table is Exponential 13:40 - Example 7: Linear Function (Constant Addition) 14:15 - Example 8: Exponential Function (Constant Multiplication) 15:00 - Exponential Growth/Decay Word Problems 15:20 - Example 9: Classic Car Value (Growth Model) 16:00 - Understanding Growth Factor & Growth Rate 16:45 - Calculating Future Value 17:00 - Example 10: Bike Depreciation (Decay Model) 17:45 - Understanding Decay Factor & Decay Rate 18:00 - Calculating Future Value 18:30 - Simplifying Expressions with Natural Base 'e' 18:45 - Example 11: (e^2 * e^3) / e^4 19:20 - Example 12: (e^10) / (e^3) 19:40 - Identifying Growth/Decay, Rate, and Initial Amount 20:00 - Example 13: y = 3 * (2/3)^x 20:45 - Example 14: y = 20 * (4/5)^(-x) (Reciprocal & Growth) 21:50 - Example 15: y = 12 * (0.92)^x 22:25 - Compound Interest & Doubling Time Word Problems 22:45 - Example 16: Compound Monthly (A = P(1 + r/n)^(nt)) 24:00 - Example 17: Compound Continuously (A = Pe^(rt)) 25:00 - Example 18: Bacteria Doubling (A = P * b^t) 25:45 - Conclusion and Additional Resources ➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos) https://www.youtube.com/channel/UClOR1BiPyOkkIAnv9Cmj4iw/join