1. 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= 𝑥 +3
3. 𝑦= 4∙2 −𝑥

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

3. Pre-Spring Break Classwork

4. 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

5. 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….

6. 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…

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

8. 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