Day 34 in Mat122

Today:

• 7.3 due Tomorrow

• Section 7.4: applications of exponential growth and decay
  • Exponentials satisfy a very important differential equation:

  • Doubling time: the time it takes for a growing exponential function to double in size.

  • Half life: the time it takes for a dying exponential function to halve in size.

  • Forget The rule of 70 (72, 71, 69.3,...):
    where n is the number of compoundings per year, and r is given as a decimal (e.g. 9% is represented by .09).

    When compounding is continuous (i.e. ), this reduces to the very lovely rule

  • Examples:
    • #9, p. 372
    • #16, p. 372
    • #18, p. 372

• Section 7.7: L'Hopital's Rule
  • Now, how do we know that ?