Warm Up Write a function to represent the amount after t years for each situation. –100 grams of a compound with a half-life of 5000 years –12 bacteria that quadruple themselves every 2 years –A new car worth $35,000 that depreciates 15% per year –A $75,000 student loan with a 6% annual interest rate. What is the equivalent annual interest rate on a “payday” loan for $500 that charges a one-time 5% processing fee + $20 per month per $100 of the loan. (consider all charges and fees as the “interest” on the loan)

Warm-up answers

Exponential equation reminders

5.3 Exponential Functions Homework Questions? Homework: Page odd, 27, 28

Section 5.4 Two new forms of the exponential function: One dealing with compound interest A 2 nd also dealing with compound interest and population models

5.4 The Function e^x Lim , , Complete the table.

Leonhard Euler euler.htmlhttp:// euler.html Leonhard Euler ( )

Some fun facts about Leonard Euler he spent most of his academic life in Russia and Germany, especially in the burgeoning St. Petersburg of Peter the Great and Catherine the Great Had a long life and thirteen children his collected works comprise nearly 900 books and, in the year 1775, he is said to have produced on average one mathematical paper every week he had a photographic memory

5.4 The Function e^x

Annually12% Semiannually 6% Quarterly3% Monthly1% Daily (365 days) (12/365)% k times per year (12/k)% Interest Period % growth each period Growth factor during period Amount e

Lim

Effective annual yield

5.4 The Function e^x

homework 1: study for your quiz: –Review homework from sections 1-3 –Chapter test: pg. 209, Start section 4: (due next week) 1-17odd, pg 209