# UNIT 1 Key Questions 1 2 3 4 5 Essay

1220 Words Nov 17th, 2014 5 Pages
Key Questions Unit 1 Lesson 1
1.
a) (2x3)(-7x5)= -14x8

b) -45x5y7z9/9x7y7z5= -5z4/x2

c) (-5x4)3= (-53)(x12)= -125x12

d) (3x4y5z7)5/(-3x3yz4)7=243y18z7/-2187x= y18z7/-9x

e) (xa+b)a-b/(xa-2b)a+2b= (xa^2-b^2)/(xa^2-4b^2)= x3b^2

2.
a)6-2= 1/62=1/36

b)253/2=(2√25)3=53=125

c) -85/3=(3√-8)5= (-2)5= -32

d) 625(-3/4)=1/(4√625)3=1/53= 1/125

3.
a) 93x272x813= (32)3x(33)2x(34)3= 36x36x312= 324

b) 57x253/1254= (57x(52)3)/(53)4= 57x56/512=513/512= 5

4.

5. To find the equation of the exponential function that pass through (0,-1),(-1,-3),(-2,-9) with x-axis as asymptote:
Formula: y=a(bx) y-intercept (0,-1)
1) Point 1 (-1,-3) 2) Point 2 (-2,-9)
(-3)=ab-1 (-9)=ab-2
-3/b-1=a (-9)/b-2=a

Find b-
Since a=a
Therefore -3/b-1=
Graph y= -2log3(x-3)-1

20. y=(1/5)log3(9x-36)15-13 y=(1/5)(15)(log3(9x-36))-13 y=3(log3(9x-36))-13 y=3(log3(9(x-4))-13 y=3(log39+log3(x-4))-13 y=3(3+log3(x-4))-13 y=9+(3log3(x-4))-13 y=3log3(x-4)-4
Transformation applied to original equation: y=log3x to become y=3log3(x-4)-4
-Vertically stretched by a factor 3
-Translated 4 units to the right
-Translated 4 units down
-D={x∊R, x>4)
-R={y∊R)
-Vertical Asymptote at x=4 (original at x=0)
-Pass through point (5,-4) (from original x-intercept at (1,0)

21. y=1000(10x) y=(103)(10x) y=103+x y=10x+3 (y=10x-(-3))

22. a)
Toss
Coins left
0
20
1
10
2
3
3
2
4
1
5
1
6
1
7
1
8
0

b) i)

ii) the equation that best fits the graph is y=P(1-b)n
P=starting number of coins, b=rate of decay=approximately 0.5, n=number of the toss iii) This experiment models exponential decay phenomena

c) If began with N0 coins, the equation would be N(n)=N0(1/2)n, N(n)=number at toss n, N0 =Initial number at toss 0, i.e. N(n)=20(1/2)n

Toss
Coins left
0
20
1
12
2
6
3
4
4
3
5
1
6
1
7
1
8
1
9
0
d)

23.a)

b) It appears exponential because the number of total coins(column 3) increases on every toss by a factor of 1.5

c)Exponential equation that best fits the results: y = P(1.5)n
P = initial number of coins, n=number of toss

d)The equation that would represent the number of coins remaining if started with N0 coins:
N(n)= N0(1.5)n ,N(n)=number at toss n, N0 =Initial number at toss