Chapter 9 Radical Functions

SSM: Intermediate Algebra
Chapter 9 Test
54. ( 3,7 ) and ( 5,4 )
Substitute the points into the equation
y a x b = + .
7 = a 3 + b
4 = a 5 + b
Rewrite as:
1.7321a
+ b = 7
2.2361a
+ b = 4
Solve the system of equations. Multiply the first
equation by − 1 and add to the second equation.
−1.7321a
− b = −7
2.2361a
+ b = 4
0.504a
= −3
a ≈ −5.95
3,7 into the equation
Substitute the point ( )
y = − 5.95 x + b and solve for b.
7 = − 5.95 3 + b
b = 7 + 5.95 3
b ≈ 17.31
The equation is roughly y = − 5.95 x + 17.31.
55. a. Start by plotting the data.
A square root model, y = a x + b , seems
reasonable.
4, 28.8 .
Use the points ( 0,16 ) and ( )
The y-intercept is ( 0,16 ) so b = 16 .
Substitute the point ( 4, 28.8 ) into the
equation y = a x + 16 and solve for b.
28.8 = a 4 + 16
2a
= 12.8
a = 6.4
( ) = 6.4 t + 16
f t
b. ( 0,16 ) ; In 1998 there were 16 million U.S.
households with a Sony PlayStation.
c. 6.4 t + 16 = 36
6.4 t = 20
t = 3.125
t ≈ 9.77
In 2008, 36 million households in the United
States will have a Sony PlayStation.
d. f ( 5)
= 6.4 5 + 16 ≈ 30.31
The model predicts a slightly larger number
of households, but the values are fairly
close.
Chapter 9 Test
1.
9 8
32x = 16x ⋅2x
=
4
8
16x
2x
= 4x
2x
2. 3 64 22 3 64
21
x = x ⋅ x
=
3 21 3
= 4x
64x
7 3
4 4
3. ( 2x + 8) = ( 2x + 8) ⋅ ( 2x
+ 8)
4.
3
4 x 2x
=
5
6 x 3x
=
2
3
x
x
27 24 3
1/ 3
1/ 5
2
= x
3
2
= x
3
1 1
x3 − 5
( 2x
8) ( 2x
8)
4 24 4
3
= + +
4
( 2x
8) ( 2x
8)
6 3
= + +
5 3
−
15 15
2/15
15 2
2 x
=
3
307