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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 -20123 F(x)
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To be able to use exponential functions to model real world data
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For this, you will be in groups of 3 to conduct a brief experiment. M&M experiment
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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.
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Half Life Doubling Time Compound Interest Continuous Compound Interest Exponential Growth/Decay Continuous Exponential Growth/Decay
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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.
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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?
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A = Pe rt P = Principal r = rate (decimal) t = time (years) Use it when: you see the words “compounded continuously”
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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?
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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”
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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.
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N = N 0 e rt N 0 = starting amount r = rate (decimal) t = time Use it when you see “continuous growth or decay”
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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.
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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
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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?
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A = P(2) t/DT P = Principal (starting amount) t = time DT = doubling time Use it when you see the words “doubling time”
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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?
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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.
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