1. Given the function f(x) = 3e x :  a. Fill in the following table of values:  b. Sketch the graph of the function.  c. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing. x F(x)

 To be able to use exponential functions to model real world data

 For this, you will be in groups of 3 to conduct a brief experiment.  M&M experiment

 Look at the patterns of the numbers you wrote down.  What’s happening in the left column? Right column?  Use L1 and L2 and Stat Plot to look at the shape your points made.

 Half Life  Doubling Time  Compound Interest  Continuous Compound Interest  Exponential Growth/Decay  Continuous Exponential Growth/Decay

 P = principal  r = rate (decimal)  n = number of times per year  t = time in years  Use it when you see: compounded yearly, quarterly, monthly, semi-annually, etc.

 Kristy invests $300 in an account with a 6% interest rate, making no other deposits or withdrawals. What will Kristy’s account balance be after 20 years if the interest is compounded  a. Semiannually?  b. Monthly?  c. Daily?

 A = Pe rt  P = Principal  r = rate (decimal)  t = time (years)  Use it when: you see the words “compounded continuously”

 Suppose Kristy finds an account that will allow her to invest her $300 at a 6% interest rate compounded continuously. If there are no other deposits or withdrawals, what will Kristy’s account balance be after 20 years?

 N = N 0 (1 + r) t  N 0 = initial amount  r = rate (decimal)  growth: r is positive  decay: r is negative  t = time (years)  Use it when: growth/decay is “per year” or “annual”

 Mexico has a population of approximately 110 million. If Mexico’s population continues to grow at 1.42% annually, predict the population of Mexico in 10 and 20 years.

 N = N 0 e rt  N 0 = starting amount  r = rate (decimal)  t = time  Use it when you see “continuous growth or decay”

 The population of a town is declining at a rate of 6%. If the current population is 12,426 people, predict the population in 5 and 10 years using the continuous model.

 A = P(1/2) t/HL  P = Principal (starting amount)  t = # of years  HL = half life  Use it when: you see the words “half life” in the problem

 The half life of a certain radioactive substance is 20 days and there are 5 grams present initially. How much will be left after 30 days?

 A = P(2) t/DT  P = Principal (starting amount)  t = time  DT = doubling time  Use it when you see the words “doubling time”

 During springtime, the rabbit population of a certain forest has a doubling time of 40 days. Suppose the forest contains 100 rabbits to begin with. How many rabbits will be in the forest after 25 days, and 90 days?

 Use your notes and study guide to help you complete the practice problems on the back of your sheet.  p. 166 # 21, 23, 25, 31, 36, 37 – 40  What you don’t finish you must finish for homework.