 Def: Asymptote – a boundary line a graph cannot cross.  NOTE: Exponential functions have horizontal asymptotes.

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Presentation transcript:

 Def: Asymptote – a boundary line a graph cannot cross.  NOTE: Exponential functions have horizontal asymptotes.

 In an equation of the form, c is the horizontal asymptote. Use your graphing calculator to graph: a) b) c) -all in the same viewing window!

 Graph:  This function has a horizontal asymptote at approximately We call this value “e”.  e is an irrational number (kinda’ like π). Discovered by Leonard Euler in the mid- 1700’s. Called it “e” for his last name initial.

 Sketch the graph of  Calculate the following:

 This formula is used in banks, stocks & finance to calculate compounded interest.  P = principle (original amount of $)  r = interest rate (%)  n = # of times compounded  t = time (in years)

 Bill takes $5000 to his bank that gives 2.3% interest. Find how much money he has at the end of 10 years if it’s compounded: a) Annually (once per year) b) Semi-annually (twice per year) c) Quarterly (4 times per year) d) Monthly (12 times per year) e) Daily (365 times per year) How often would a bank have to compound money in order for Bill to get the MOST MONEY POSSIBLE?

 The formula is used for CONTINUOUS compounded interest. This will give you the maximum amount of money.  Bill takes $5000 to his bank that gives 2.3% interest. Find how much money he has at the end of 10 years if it’s compounded continuously.  Andy takes $150,000 and puts it into a stock averaging 4.7% interest. How much money will he have at the end of 30 years of investing if it’s compounded continuously?

 Mary needs $100,000 in 30 years to buy a vacation home when she retires. How much would she have to invest TODAY at 3.1% compounded continuously?  How much would you need to invest today to become a millionaire when you’re 60 years old (invested at 8.2% CC)