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Applications of Exponential Functions

Applications of Exponential Functions. THE GENERAL EXPONENTIAL FUNCTION. y = amount after a certain time c = initial amount a = growth factor t = time n = time it takes for a growth factor of “a”. EXAMPLE 1: Doubling time.

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Applications of Exponential Functions

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  1. Applications of Exponential Functions

  2. THE GENERAL EXPONENTIAL FUNCTION • y = amount after a certain time • c = initial amount • a = growth factor • t = time • n = time it takes for a growth factor of “a”

  3. EXAMPLE 1: Doubling time • A bacteria culture starts out with 200 bacteria. It doubles every 5 hours. a) Fill in the table of values:

  4. EXAMPLE 1: Doubling time • A bacteria culture starts out with 300 bacteria. It doubles every 5 hours. a) Fill in the table of values:

  5. Sketch the function:

  6. EXAMPLE 1: Doubling time • A bacteria culture starts out with 300 bacteria. It doubles every 5 hours. • c) State the equation of N with respect to t.

  7. EXAMPLE 1: Doubling time • A bacteria culture starts out with 300 bacteria. It doubles every 5 hours. • d) Find the number of bacteria after 19 hours.

  8. EXAMPLE 2: Half Life(the amount of time it takes for a mass to become half of what it was originally) • Living organisms contain radioactive carbon-14, which has a half-life of 5730 years once the organism dies. A 100g sample of a tree is studied. a) Fill in the table of values:

  9. EXAMPLE 2: Half-life a) Fill in the table of values:

  10. Sketch the function:

  11. EXAMPLE 2: Half-life • c) State the equation of m with respect to t.

  12. EXAMPLE 2: Half-life • d) Find the mass after 10000 hours

  13. EXAMPLE 3:Value of a sports car • SpongeBob buys a Ferrari for $20,000. It appreciates at 7% per year. a) Fill in the table of values:

  14. EXAMPLE 3:Value of a sports car a) Fill in the table of values:

  15. Sketch the function:

  16. EXAMPLE 3:Value of a sports car • c) State the equation of V(value) with respect to time t.

  17. EXAMPLE 3:Value of a sports car • d) Find the value after 25 years

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