Negative & Zero Exponents

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Presentation transcript:

Negative & Zero Exponents

Agenda New seating plan Homework Check Warm up Review Patterns in Powers Radioactive Decay TOC

Warm up Seating Plan Homework Check Mr. and Mrs. Wright

y = 2(x+1)(x-7) (-1,0) (7,0) (3, -32)

y = 2(x+1)(x-7) Find the zeroes of the parabola -1 & 7 Find the axis of symmetry x = (-1+7) = 6 = 3 x = 3 2 2 Find the vertex coordinates y = 2(3+1)(3-7) = 2(4)(-4) = 8(-4) = -32 (3, -32)

Patterns in Powers What pattern do you observe between the consecutive answers? Will this ever reach a value of 0? What does this look like on a graph? Power of 2 Evaluate 25 32 24 16 23 8 22 4 21 2 20 1 2-1 ½ = 0.5 2-2 ¼ = 0.25 2-3 1/8 = 0.125 2-4 1/16 = 0.0625 2-5 1/32 = 0.03125

Plotting 2x

Exponent Laws Fill out the following table, and write a rule for a base raised to a negative exponent Expression Expand and Divide Exponent Law 33 35 3 x 3 x 3 = 1 = 1 3 x 3 x 3 x 3 x 3 3 x 3 32 33 = 33-5 = 3-2 41 43 4 = 1 = 1 4 x 4 x 4 4 x 4 42 41-3 = 4-2 24 27 2 x 2 x 2 x 2 = 1 = 1 2 x 2 x 2 x 2 x 2 x 2 x 2 2 x 2 x 2 23 24-7 = 2-3 (-5)2 (-5)3 (-5) (-5) = 1 (-5) (-5) (-5) (-5) (-5)2-3 = (-5)-1 (-2)3 (-2)5 (-2) (-2) (-2) = 1 = 1 (-2) (-2) (-2) (-2) (-2) (-2) (-2) (-2)2 (-2)3-5 = (-2)-2

Exponent Laws Fill out the following table, and write a rule for a base raised to the exponent 0 Expression Expand and Divide Exponent Law 35 3 x 3 x 3 x 3 x 3 = 1 3 x 3 x 3 x 3 x 3 33 = 33-3 = 30 33 52 5 x 5 = 1 5 x 5 52-2= 50 43 4 x 4 x 4 = 1 4 x 4 x 4 43-3 = 40 (-3)4 (-3) (-3) (-3) = 1 (-3) (-3) (-3) (-3)4-4 = (-3)0 (-2)2 (-2) (-2) = 1 (-2) (-2) (-2)2-2 = (-2)0

Radioactive Decay Carbon-14 is a radioactive element that decays to 1/2 , or 2-1, of it’s original amount after every 5700 years. Determine the remaining mass of 10 g of carbon-14 after A) 11 400 years B) 28 500 years

Radioactive Decay 11 400 = 2 (2 half lives) 5700 10 x 2-2 = 10 x 1 = 10 x ¼ = 2.5 22 28 500 = 5 (5 half lives) 10 x 2-5 = 10 x 1 = 10 x 1 = 0.3125 25 32

TOC If any number is raised to the power 0, the answer is ___ Homework Pg. 199 Q # 1, 2, 6, 11, 14 Chapter Review tomorrow & Friday!