what’s so special about ‘e’? - department of …...what’s so special about ‘e’? •here...

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Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012 What’s so special about ‘e’? • Here is the full formula if they compute interest ‘n’ times per year at ‘r%’ annual interest beginning with P dollars. • So the “annual multiplying factor’ is • And when ‘n’ gets bigger and bigger, this multiplying factor gets closer and closer to

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Page 1: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

What’s so special about ‘e’?

• Here is the full formula if they compute interest ‘n’ times per year at ‘r%’ annual interest beginning with P dollars.

• So the “annual multiplying factor’ is

• And when ‘n’ gets bigger and bigger, this multiplying factor gets closer and closer to

Page 2: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Compounded Interest Formulas

• If the annual interest rate is ‘r %’ and it is compounded ‘n’ times each year for ‘t’ years the amount is

• If the annual interest rate is ‘r %’ and it is compounded continuously for ‘t’ years the amount is

• Suppose you invest $1000 in a bank that offers 12% interest compounded monthly. How much interest do you get the first month? How much the second month? How much is your account worth after 1 year? After 10 years?

Page 3: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

• Suppose you invest $1000 in a bank that offers 12% interest compounded continuously? How much is your account worth after 1 year? After 10 years?

Page 4: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Suppose you know that there are initially 2000 bacteria in a petri dish in a lab. Also the population increases by 50% every 3 hours.Find a formula for the population of bacteria after t hours.

Page 5: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Homework ProblemsSec. 4.1 # 67

A sky diver jumps from an airplane. The air resistance is proportional to her velocity and the ratio is 0.2. Her downward velocity is given by

Where ‘t’ is in seconds and ‘v(t)’ is feet/sec.• Find the initial velocity of the skydiver.

• Find the velocity after 5 seconds.

• Find the velocity after 10 seconds.

• Graph the velocity function.

• What is the terminal velocity of the diver?

Page 6: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Page 7: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Page 8: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Page 9: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

Page 10: What’s so special about ‘e’? - Department of …...What’s so special about ‘e’? •Here is the full formula if they compute interest ‘n’ times per year at ‘r%’

Sec41NotesExponentialFunctionsDonePart2.notebook October 18, 2012

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