What do you remember about the following:  1) What is factoring? Give an example.  2) What exponent rules do you remember? Give examples (there are 5).  REMINDERS:  Sign up for Remind.com The code is on the class web site.  Check out tutoring times on web site, remind texts, front white board, outside the door.

6.1 Notes: Growth and Decay Functions

What is an exponential growth function?  The variable is in the exponent rather than the base.  Exponential growth increases slowly at first, then drastically increases as time continues.  The basic graph looks like:

Basic Graph info:  Equation: f(x) = b x, where b > 1  With a “go-to” point (always passes through) at (0, 1)  Horizontal asymptote at y = 0.  Wait…what’s an “asymptote?”…….it’s a line that the graph will never cross, only approach forever.  How do we evaluate an exponential growth function?  We pick some values for “x” and plug them in

Exponential Decay  What is an exponential decay function? There is a rapid decrease initially and then the decrease becomes more gradual.  Equation: f(x) = b x, where 0 < b < 1 (basically, they are fractions).  The basic graph has the same go – to point at (0, 1) and asymptote at y = 0.  The base is between 0 and 1.  The graph looks like:

Graphing: Pick at least 3 values for x, plug them in to find y. Graph the points  EX A: y = 2 x B: y = 3 x  x f(x)x f(x)

Evaluating exponential decay functions:  EX A: f(x) = (½) x B: y =  x f(x)x f(x)

Solving Real-world problems:

HW: p. 300 #3 - 22

Warm Up:

Exponential Models:  Exponential growth model: y = a(1 + r) t  y = amount after increase  a = initial amount  r = percent increase written as a decimal  t = # of years  EX: y = 25,000( ) 5  EX: In 2000, the world population was about 6.09 billion. During the next 13 years, the world population increased by about 1.18% each year. Write an exponential growth model giving the population y (in billions) t years after Estimate the population in 2005.

Exponential Models:  Exponential decay model: y = a(1 - r) t  y = amount after decrease  a = initial amount  r = percent decrease written as a decimal  t = # of years  Example: y = 15,500(1 – 0.17) 7  Example: You purchased the new BMW 3 Series car for $35,357. The car depreciates at a rate of 13 percent per year. Write an equation to model the drop in value of the car, then determine the value of the car in 6 years.

Compund Interest:  Interest is the money earned on an investment. This could be a bank account, certificate of deposit, stocks, bonds, loan to someone, etc. Depreciation is the money lost over time on something purchased. The most thorough of example for this is a car.  Interest: Interest can be compounded (calculated) once a year, twice a year, three times a year, etc, up to continuously. We will use the compound interest formula:

 If we compound:we calculate interest (per year):  Quarterly4 times  Monthly12 times  Bi-monthly24 times  Weekly52 times  Daily365 times  EX: You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest is compounded a) quarterly and b) daily.

DUE in class: p. 315 # ,