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Extra 5 point pass if you can solve (and show how)…

Extra 5 point pass if you can solve (and show how)…. Find the inverse of: *10 minute limit!!!. 3.2 – Logarithmic Functions and Their Graphs. Some things to ponder…. What are the properties of exponential functions that we learned yesterday?

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Extra 5 point pass if you can solve (and show how)…

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  1. Extra 5 point pass if you can solve (and show how)… • Find the inverse of: *10 minute limit!!!

  2. 3.2 – Logarithmic Functions and Their Graphs

  3. Some things to ponder…. • What are the properties of exponential functions that we learned yesterday? • Who remembers how to determine if a function has an inverse? • Will an exponential function have an inverse?

  4. y = axhas an inverse logax=y • y = axis equivalent to logay=x • Remember that logs are exponents…. So logax is the exponent to which “a” must be raised to obtain x

  5. Ex. 1) log28=? • Ex. 2) log232=? • Ex 3) log10(1/100)=?

  6. Log4774000=? • 55x=22500

  7. Graphing Logs… • y=logax Domain: (0,∞)Range: (- ∞, ∞ ) x intercept: (1,0) increasing: (- ∞, ∞)

  8. Graph f(x)=log2x

  9. Graph f(x)=log3x + 4

  10. Transformations….. • f(x)=logbx g(x)= alogb(c(x-h))+k • The transformations are the same for “a”, “c”, “h”, and “k” for all the other functions we have studied….*absolute value, quadratic, exponential, etc.

  11. Natural Log Function… • f(x)=logexlnx • y=ex and y = lnx are inverses • y=lnx implies ey=x

  12. Properties… • e0= • e1= • ln ex= • elnx= • ln(1)= • ln(0)= • ln(-1)= • If lnx = lny then

  13. Simplify with out a calculator: • (a) ln • (b) e ln5 • (c) • (d) 2 lne

  14. Day 1 - HW • pg. 216 #’s 1 – 52 (3’s)

  15. Bacteria in a bottle… • There is a single bacterium in a bottle at 11:00pm, and it is a type that doubles once every minute. The bottle will be completely full of bacteria at 12:00 midnight – exactly one hour. • In your opinion, what percentage of the bottle will be full when the bottle starts to look full? For what amount of time between 11:00 and 12:00 would they have plenty of room to grow and spread out? If you were a researcher in the lab, at what time between 11:00 and midnight might make you look in the bottle and think “I’d better get a bigger container for those bacteria!”?

  16. Finding Domain of Ln Functions… • f(x)=ln(x-2) *think about the properties of ln • g(x)=ln(2-x) • h(x)=lnx2

  17. Lets do the application (ex 10) on page 215 together… Graph #41 on page 216 Practice Problems to work on now pg. 216 #’s 20, 24, 26, 43, 47, 57, 59, 60, 61

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