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Understanding Exponential Functions: Growth Beyond Linearity

Learn how exponential functions model growth such as population and compound interest. Explore continuous compounding and properties of exponents to solve equations and find constants in curves.

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Understanding Exponential Functions: Growth Beyond Linearity

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  1. Math 140 4.1 – Exponential Functions; Continuous Compounding

  2. Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest).

  3. Some things just don’t grow linearly, they grow exponentially (ex: population, compound interest). U.S. Population Source: http://en.wikipedia.org/wiki/File:US_Population,_1790_-_2011.svg

  4. To model such behavior, we use the exponential function, . is the base (, ). ex: ex:

  5. Natural Exponential Base: (Amount of money you’d have in an account if you invested $1 at 100% interest rate per year for one year, where interest is compounded continuously.)

  6. In general, the continuously compounded interest formula is , and the regular compound interest formula is .

  7. Properties of exponents:

  8. Ex 1. Evaluate: Ex 2. Solve: Ex 3. Solve:

  9. Ex 4. Find values of the constants and so that the curve contains and .

  10. Ex 4. Find values of the constants and so that the curve contains and .

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