UNIT 1 Key Questions 1 2 3 4 5

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= (-9)/b-2
-3(b-2)= -9(b-1)
-3(b-2)-9(b-1)=0
b-1(-3b-1-9)=0

b-1=0 or (-3b-1-9)=0
1/b=0 -3b-1=9
1(0)=b b-1=3 b=0 1/b=3 1=3b b=1/3
Since the plotted curves of exponential function never go above the x-axis, b must equal 1/3

Find a- a=-3/(b-1) a=-3/(1/3)-1 a=-3/(1/(1/3)) a=-3/(1x3) a=-1 The equation of the exponential function that pass through (0,-1),(-1,-3),(-2,-9) with x-axis as asymptote is y= -(1/3)x

6. Formula- C(t)=C0(2)-t/H
C(t)=75
C0=2400
H= 13.8sec
75=2400(2)-t/13.8
75/2400=(2)-t/13.8
1/32=(2)-t/13.8
1/(25) =(2)-t/13.8
2-5=(2)-t/13.8
-5= -t/13.8
(-5)(-13.8)=-t
-69=-t t=69 It will take 69sec for 2400g of Beryllium-11 to decompose into 75g of Beryllium-11

7. Formula- A=P(1+i)n
P=20000
i= -0.3 n=5 A=20000(1+(-0.3))5
A=20000(0.7)5
A=3361.40
It will be worth 3361.40 after 5 years

Key Questions Unit 1 Lesson 2
8.
a) log636=2

b) log6(1/36)= -2

c) 7log^7(12)=71.276989=12

d)log168=0.75 or 3/4

e)log381√27=(34)(√33)=(34)(33)1/2=(34)(33/2)=311/2=11/2

f)log1/31=0

9.
a)log7x=2
x=72 x=49 b)logx64=3 x3=64 x=4

c)log3(2x-1)=3
33=2x-1
27=2x-1
28=2x
x=14

10.
a)log82+log832=(1/3)+(5/3)=6/3=2

b)log5150-log56=log5(150/6)=log525=2

c)log520+log510-3log52=log5(20x10)-3log5(2)
= log5(20x10)-log5(23)= log5(20x10/8)= log5(25)