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SS.01.7 - Solving Exponential Equations

SS.01.7 - Solving Exponential Equations. MCR3U - Santowski. (A) Review. If two powers are equal and they have the same base, then the exponents must be the same ex. if b x = a y and a = b, then x = y. If two powers are equal and they have the same exponents, then the bases must be the same

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SS.01.7 - Solving Exponential Equations

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  1. SS.01.7 - Solving Exponential Equations MCR3U - Santowski

  2. (A) Review • If two powers are equal and they have the same base, then the exponents must be the same • ex. if bx = ay and a = b, then x = y. • If two powers are equal and they have the same exponents, then the bases must be the same • ex. if bx = ay and x = y, then a = b.

  3. (B) Using this Property in Exponential Equations • This prior observation set up our general equation solving strategy => get both sides of an equation expressed in the same base • ex. Solve and verify (½)x = 42 - x • ex. Solve and verify 3y + 2 = 1/27 • ex. Solve and verify (1/16)2a - 3 = (1/4)a + 3 • ex. Solve and verify 32x = 81 • ex. Solve and verify 52x-1 = 1/125 • ex. Solve and verify 362x+4 = (1296x)

  4. (B) Using this Property in Exponential Equations • The next couple of examples relate to quadratic equations: • ex. Solve and verify 2x²+2x = ½ • ex. Solve and verify 22x - 2x = 12

  5. (C) Examples with Applications • Example 1  Radioactive materials decay according to the formula N(t) = N0(1/2)t/h where N0 is the initial amount, t is the time, and h is the half-life of the chemical, and the (1/2) represents the decay factor. If Radon has a half life of 25 days, how long does it take a 200 mg sample to decay to 12.5 mg?

  6. (C) Examples with Applications • Example 2  A bacterial culture doubles in size every 25 minutes. If a population starts with 100 bacteria, then how long will it take the population to reach 2,000,000?

  7. (C) Homework • Nelson text p94, Q1,3,4 (concept) 6-9eol, 14, 17,18 (application) • AW text, p51, Q9, 10, 12

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