Exponential Function Week 25 Lesson 3

Exponential Function Week 25 Lesson 3

By Dr Kee

Open Ended

2.71828182845904523536028747135266249775724709369995...

What is so "special" about this irrational number?

REVISION

Open Ended

Name ONE difference between simple and compound interest.

Simple Interest Formula $$A=P\left(1+rt\right)$$  

Compound Interest Formula $$A=P\left(1+\frac{r}{n}\right)^{nt}$$  

Draw

If you are earning 10% interest, compounded weekly, and your goal is have $3000 in your account after six years, how much will you have to initially deposit?

Draw

If you are earning 7% interest, compounded

The Constant, e

e = 2.71828182845904523536028747135266249775724709369995...

Replace this text with your title

Some text here about the topic of discussion

Let's Explore!

You will need your calculator for this task.

​Use your calculator to complete this table.

​

e is an irrational number!

2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931277361782154249992295763514822082698951936680331825288693984964651058209392398294887933203625094431173012381970684161403970198376793206832823764648042953118023287825098194558153017567173613320698112509961818815930416903515988885193458072738667385894228792284998920868058257492796104841984443634632449684875602336248270419786232090021609902353043699418491463140934317381436405462531520961836908887070167683964243781405927145635490613031072085103837505101157477041718986106873969655212671546889570350354...

Your task - find e on your calculator.

Can you?

Continuous Compounding

Draw

Circle the e on the calculator

Continuous Compouding

We now are able to simplify the continuous compounding of interest (n going to infinity).

Continuous Compouding

Continuous Compouding

Draw

What will your bank balance be if you put $600 in your account and earn 5% annual interest, compounded continuosly, for seven years?

Hint: $$A=Pe^{rt}$$  

# Quick Quiz #

Multiple Choice

Which equation describes your bank balance if $1000 earns 6% annual interest, compounded continuously, for 7 years?

• $$A\left(7\right)=1000e^{0.42}$$  

• $$A\left(7\right)=1000e^{0.06}$$  

• $$A\left(7\right)=1000\left(1+e\right)^{0.6}$$  

• $$A\left(7\right)=1000\left(1+e^{0.6}\right)^7$$  

Multiple Choice

Which equation describes your ending bank balance if $500 earns 9% annual interest, compounded continuously, for 3 years?

• $$A\left(3\right)=500\left(1+e^{0.09}\right)^3$$  

• $$A\left(3\right)=500e^{0.0027}$$  

• $$A\left(3\right)=500\left(1+e\right)^{0.27}$$  

• $$A\left(3\right)=500e^{0.27}$$  

Draw

What will be your bank balance if you put $1800 in your account and earn 4% annual interest, compounded continuously for six years?

$$A=Pe^{rt}$$  

Draw

What will be your bank balanace if you put $3000 in your account and earn 2% annual interest, compounded continuously for 10 years?

$$A=Pe^{rt}$$  

HOMEWORK

Please check Microsoft Teams​

Poll

Let's reflect!

• I can use the scientific calculator to evaluate interest.

• I can tell the difference between simple interest and compound interest.

• I can describe the constant e and how it is used in the continuous compounding of interest.