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Midterm Review Tues Jan 21

Midterm Review Tues Jan 21. Find the inverse of 1) f(x) = 3x - 1 2) g(x) = (x+1)^2. Midterm Review Thurs Jan 23. Find the domain 1) y = (x+2)^1/2 2) log [(5-x) / (x – 7) ]. 4.6 word problems with e^x and logx. Exponential growth and decay Y = P e^( kt ) P = initial amount (principal)

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Midterm Review Tues Jan 21

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  1. Midterm ReviewTues Jan 21 Find the inverse of 1) f(x) = 3x - 1 2) g(x) = (x+1)^2

  2. Midterm ReviewThurs Jan 23 • Find the domain • 1) y = (x+2)^1/2 • 2) log [(5-x) / (x – 7) ]

  3. 4.6 word problems with e^x and logx • Exponential growth and decay • Y = P e^(kt) • P = initial amount (principal) • K = growth / decay factor • T = time

  4. Interest formula • Continuously compounded • A = P e^(kt) • Compounded “N” times per year • A = P (1 + k/N)^(Nt)

  5. Ex1 - interest • We put $10,000 into an account paying 7% interest. How much money is in the account after 5 years if • (A) interest is compounded continuously? • (B) interest is compounded monthly?

  6. Exp growth • The population of squirrels in Princeton…in 2000 there were 5,000 squirrels. If there are currently 7500 squirrels in 2014, approximately how many will there be in 2020?

  7. Exp decay - halflife • Carbon-14 has a half-life of 5750yrs. If 50 g of carbon-14 has decayed to 20g, how old is this carbon-14?

  8. 1.5 increasing,decreasing, relative min/max • Increasing = positive slope • Decreasing = negative slope • Constant = 0 slope • Relative minimum = - slope to + slope • Relative maximum = + slope to – slope • Left to right • You can have more than 1 max, min

  9. ex • Determine where a f(x) = x^3 – 3x^2 + 1 has a relative min and relative max

  10. Solving exponential equations • 1) rewrite both sides as the same base • Set both exponents equal to each other • 2) use logarithm to both sides to get x out of the exponent • 2 diff bases with x’s • 1 base with x

  11. Exp ex 1 • Solve for x • 9^x = 1/27

  12. Exp ex 2 • Solve for x 6^(2x-1) = 12

  13. Exp ex3 • Solve for x 2^x = 5^(x-1)

  14. Logarithmic equations • 1) 1 log = ‘exponentiate’ both sides • 2) 2 log = set the 2 logs equal to each other, and then cancel out the logs • 3) 2 logs and a non-log, or more than 2 logs • Combine logs, then #1/2

  15. Log eq ex1 • Solve for x 2 = log8 (2x – 5)

  16. Log eq ex2 • Solve for x ln (x-1) - ln (3x+1) = 0

  17. Log eq ex3 • Solve for x log2 (x + 1) + log2 (x -2) = 2

  18. Even/odd functions • Odd functions • If f(-x) = -f(x) • Symmetric about the origin • Will only have odd powers • Even functions • If f(-x) = f(x) • Symmetric about the y-axis • Will only have even powers

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