Daily Check If f(x) = x2 + 4 and g(x) = 3x + 2, find the following: f(g(x)) g(f(2) f(g(-3))

EOCT Practice Question of the Day

EOCT Practice Eddie wants to build a slide in his backyard from his bedroom window to the edge of his pool. His window is 30 feet from the ground. The angle created by the ground and the slide is 41°. How long will his slide need to be? Round your answer to the nearest tenth. 39.8 feet 34.5 feet 19.7 feet 45.7 feet

Homework Review

How do you model growth and decay? Math II Day 53 (10-23-10) Standard MM2A2: C – Graph functions as transformations of f(x) = ax E – Understand and use basic exponential functions as models of real world phenomena. Today’s Question: How do you model growth and decay?

Graphing Exponential Functions y = 4x+3

y = 4x+3 x 4x+3 y (x,y) -8 4-8+3 .0009 (-8, .0009) -5 4-5+3 .0625 (-5, .0625) -2 4-2+3 4 (-2, 4) 40+3 64 (0, 64) 1 41+3 256 (1, 256)

Do you see what happens at the X axis. Asymptote Domain: [-∞,+∞] Range: [0,+∞]

y = - 4x+3 + 6 negative sign will flip it on the x axis 4 will make it narrow ¼ will make it fat X+3 moves the graph to the left 3 units +6 moves the graph up 6 units. (moves the asymptote)

You try….. y = 2x-3 + 1 x 2x-3+1 y (x,y) -2 2-2-3+1 1.03 (-2, 1.03) -1 2-1-3+1 1.06 (-1, 1.06) 20-3+1 1.125 (0, 1.125) 4 24-3+1 3 (4, 3) 6 26-3+1 9 (6, 9) x 2x-3+1 y (x,y) -2 -1 2 6

Growth

Exponential Models y = balance P = initial t = time period r = % of increase 1+r = growth factor y = balance P = initial t = time period r = % of decrease 1- r = decay factor

y = 1 (1 + 1.00)x y = 1 (2)x y = 2x Bacteria How many bacteria do we start with? 1 originally What rate is bacteria increasing at? 100% or 1 y = 1 (1 + 1.00)x y = 1 (2)x y = 2x

You try….. y = 2x x 2x y (x,y) -2 2-2 .25 (-2, .25) -1 2-1 .5 (-1, .5) 20 1 (0, 1) 4 24 16 (4, 16) 6 26 64 (6, 64) x 2x y (x,y) -2 -1 2 6

15 days later… y = 2x y = 215 y = 32,768

Decay Weird,_Crazy,_Stupid_and_Funny_Car_Crashes_[www.keepvid.com].mp4

Depreciation y = 800(1-.10)t y = 800(0.90)5 After 5 years, $472.39 A new all-terrain vehicle costs $800. The value decreases by 10% each year. Write an exponential decay model for the value of the ATV (in dollars) after t years. Estimate the value after 5 years. y = 800(1-.10)t y = 800(0.90)5 After 5 years, $472.39

Falling Leaves y = 1250(1-.18)t y = 1250(0.82)5 On a fall day the wind is blowing good and leaves are falling. One tree started off with 1250 leaves at 6:00AM. Every hour the wind is blowing off 18% of the tree’s leaves. Write an exponential decay model for the number of leaves left on the tree at 3:00PM. y = 1250(1-.18)t y = 1250(0.82)5 After 9 hours, 210 leaves on tree

In 1990, the cost of tuition at a state university was $4300 In 1990, the cost of tuition at a state university was $4300. During the next 8 years, the tuition rose 4% each year. Write a model the gives the tuition y (in dollars) t years after 1990. What is the growth factor? How much would it cost to attend college in 2000? In 2007? How long it will take for tuition to reach $6000? y = 4300(1+.04)t 1.04 2000 = $6,365 2007 = $8,376 6000 = 4300(1+.04)t Guess and Check 9 years

Classwork Book Page 122 #1 – 9, #13 – 15

Homework Page 123 # 1, 2, 3