Exponential Growth, Decay, Logarithms, and Limited Growth Functions

Course Logistics and Academic Responsibility

• Announcements: The primary method of communication for course changes, new modules, assignments, due date changes, or office hour cancellations. Students are responsible for ensuring notifications are turned on in their Canvas account.

• Discussion Post Due Date: Module 2 discussion topic is due tonight, September 24, at 11:59 PM. Module 3 discussion is also encouraged to be completed soon, although its specific due date was not announced prior.

Review of Exponential Functions: Compound Interest

• Formulas: These concepts were covered in previous weeks and quizzes revealed significant confusion.

  • Compound Interest (Discrete): $A = P_0 (1 + \frac{r}{m})^{mt}$

  • Continuous Compounding: $A = P_0 e^{rt}$

• Definitions of Variables:

  • $P_0$ (or $P$): Principal, the initial amount invested or starting capital.

  • $r$: Annual interest rate, always expressed as a decimal (e.g., 6.25% becomes $0.0625$).

  • $m$: Number of compounding periods per year.

    • Yearly: $m = 1$

    • Semi-annual: $m = 2$

    • Quarterly: $m = 4$

    • Monthly: $m = 12$

    • Weekly: $m = 52$

    • Daily: $m = 365$

  • $t$: Time period in years.

• Choosing the Correct Formula:

  • Use the discrete compounding formula when there's a specific number of compounding periods per year.

  • Use the continuous compounding formula when the problem specifies