Assignment, pencil, red pen, highlighter, calculator U3D2 Have out: The average price for a 12 pack of soda is $3.99. Suppose the average annual rate of inflation is 3.2%. Answer the following. Bellwork: a) Write an equation V(t) for the value of the 12 pack after t years. V(t) = 3.99(1.032)t +2 b) What is the expected price of the pack in 6 years? V(6) = 3.99(1.032)6 +1 The price will be about $4.82 in 6 years. V(6) ≈ $4.82 +2 c) What was the price of the soda 7 years ago? (Hint: think negative exponents) The price was about $3.20 seven years ago. V(–7) = 3.99(1.032)–7 +1 V(–7) ≈ $3.20 total: +2

You have four minutes to complete the Powers Worksheet. You may use a calculator (or the one between your ears).

Be able to recognize: THE POWERS OF 2 20= 21= 22= 23= 24= 25= 26= 27= 28= 29= 210= 1 2 4 8 16 32 64 128 256 512 1024 THE POWERS OF 3 30= 31= 32= 33= 34= 35= 1 3 9 27 81 243 THE POWERS OF 4 40= 41= 42= 43= 44= 45= 1 4 16 64 256 1024 THE POWERS OF 5 50= 51= 52= 53= 54= 1 5 25 125 625

Be able to recognize: THE POWERS OF 6 60= 61= 62= 63= 64= 1 6 36 216 1296 THE POWERS OF 7 70= 71= 72= 73= 74= 1 7 49 343 2401 THE POWERS OF 8 80= 81= 82= 83= 84= 1 8 64 512 4096 THE POWERS OF 9 90= 91= 92= 93= 94= 1 9 81 729 6561 THE POWERS OF 10 100= 101= 102= 103= 104= 1 10 100 1000 10,000

a) & b) Complete the table on the left and go up to 60 years. FX – 18 When a radioactive isotope undergoes decay, it does so at a fixed rate. The time it takes for half of its decay is called the “half-life.” For example, if a substance has a half-life of ten years, and you start with 100 grams of it, after ten years you will have only 50 grams. In another 10 years, half of the 50 grams will decay, and so on. Years Amount left 100 10 50 20 30 40 60 a) & b) Complete the table on the left and go up to 60 years. 25 12.5 6.25 3.125 1.5625

The graph should be continuous. FX – 18 c) Sketch a graph to represent this situation. Is the graph continuous or discrete? Years Amount left 100 10 50 20 30 40 60 The graph should be continuous. 10 20 30 50 40 60 Years Amount left (grams) 80 100 120 25 12.5 6.25 3.125 1.5625

d) How much will be left after 25 years? FX – 18 10 20 30 50 40 60 Years Amount left (grams) 80 100 120 d) How much will be left after 25 years? Let x = # of decades ≈ 17.67 g There will be about 17.67 grams left after 25 years. e) When will the isotope disappear completely? The isotope will never disappear completely. f) Explain why you think most states will not allow radioactive materials to be dumped inside their borders. Radioactive material never disappears.

a) What is the multiplier? FX – 19 Suppose a videotape loses 60% of its value every year it is in a video store. The initial value of the videotape was $80. a) What is the multiplier? 100% – 60% = 40% = 0.40 b) What is the value of the video after one year? V(1) = 80 (0.40)1 The video will be worth $32 in one year. V(1) = $32 c) What will the value be after four years? V(4) = 80 (0.40)4 The video will be worth about $2.05 in four years. V(4)  $2.05 d) Write a function V(t) to represent the value in t years. V(t) = 80 (0.40)t e) When does the video have no value? The video will always have a value, albeit, a very small value in the years to come.

Sketch a graph of this function. Be sure scale and label your axes. FX – 19 Sketch a graph of this function. Be sure scale and label your axes. 10 30 40 50 60 70 20 80 1 2 3 4 5 6 7 8 Years Value ($) V(t) = 80 (0.40)t

Finish today's assignment: FX 1 8- 27