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Understanding Exponential Functions: Graphing, Solving Equations, and Real-life Applications

Learn about exponential functions, plotting points, graphing, solving equations, and applying them in real-life scenarios like compound interest. Understand transformations, reflections, and continuous compounding. Explore how to find an equation passing through a point and calculate future values with different compounding intervals. Enhance your knowledge of exponential growth and decay.

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Understanding Exponential Functions: Graphing, Solving Equations, and Real-life Applications

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  1. Chapter 4(1)Exponential Functions

  2. Exponential Functions These are functions that have the variable as an exponent.

  3. Plotting points and graphing (0, 1) (1, 3) (2, 9) Always through (0,1) Never reaches y = 0 Numbers larger than 1 to a power look like this

  4. Plotting points and graphing (0, 1) (1, 1/2) (2, 1/4) Always through (0,1) Never reaches y = 0 Positive Fractions to a power look like this

  5. All transformation rules apply Moves up a units Moves down a units Moves left a units Moves right a units Reflects across the x-axis Reflects across the y-axis

  6. Sketching graphs

  7. Solving Exponential Equations Make the bases the same Set exponents equal and solve

  8. Solving Exponential Equations Make the bases the same Set exponents equal and solve

  9. Finding an equation through a point

  10. Applications: Compound Interest A = Amount you end with P = Principal (start amount) r = interest rate as a decimal n = number of times each year interest is paid (annual n = 1, monthly n = 12, weekly n = 52, daily n = 365) t = number of years How much will you have if you invest $10,000 at 8% for 40 years compounded monthly?

  11. Continuous Interest A = Amount you end with P = Principal (start amount) e = 2.71828… r = interest rate as a decimal t = number of years How much will you have if you invest $10,000 at 8% for 40 years compounded continuously?

  12. How much will you have if you invest $6,000 at 12% for 20 years compounded weekly? What annual rate will make $5000 grow to $9000 in 5 years?

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