Warm Up – 4/22 - Tuesday State the following information about the graph: Horizontal Asymptote Y-intercept Growth/Decay Draw a sketch of each 1. 𝑦= 3 𝑥 −1 2. 𝑦= 1 2 𝑥 +3 3. 𝑦= 4∙2 −𝑥

Review Interest problems: 𝐴= 𝐴 0 1+ 𝑟 𝑛 𝑛𝑡 Half-Life Problems: 𝐴= 𝐴 0 1+ 𝑟 𝑛 𝑛𝑡 Half-Life Problems: 𝐴= 𝐴 0 1 2 𝑡/ℎ

Pre-Spring Break Classwork

Compounding Methods Is compounding better or worse? Let’s do a simple example… Suppose I deposit $100 into a bank account at 6% interest. How much money will I have at the end of 1 year if a compound: A) Yearly B) Quarterly C) Monthly D) Daily

Compounding Continuously The more I compound the more money I get. We want to increase 𝑛 as high as we possibly can. We could compound minutely: 525,600 minutes in a year We could compound by secondly: 31,536,000 seconds in a year We could compound millisecondly….

Compounding Continuously The idea is that in our equation: 𝐴=𝑃 1+ 𝑟 𝑛 𝑛𝑡 1+ 𝑟 𝑛 𝑛𝑡 , we want to make n as large as possible. When we do we get a very specific number. =𝑒=2.718…

Compounding Continuously We change our equation to reflect a “continuous” compounding or a compounding that does not stop. 𝐴=𝑃 𝑒 𝑟𝑡

Example Bill deposits $300 into a bank account that is compounded continuously at a rate of 5%. How much money will he have at the end of 2 years. 𝑃=$300 𝑟=0.05 𝑡=2 𝑦𝑒𝑎𝑟𝑠