Download Unit 7 review

Algebra I
Unit 7 Review
Unit 7 Review
1) A population of bacteria triples in size every
day.
a) Model the bacteria population with an
exponential function.
b) If the initial population of the bacteria is 125
cells, what will the population be after 25 days?
Unit 7 Review
1) A population of bacteria triples in size every 5
days.
a) Model the bacteria population with an
exponential function.
y = 125 · 3x
where x is the number days
b) If the initial population of the bacteria is 125
cells, what will the population be after 25 days?
30,375 cells
Unit 7 Review
Unit 7 Review
= 251/2
= 271/3
= x3/4
Unit 7 Review
3) Simplify using positive exponents.
a) (x -2 y -4)-3 (y7 y3)
b)
(2x5)3
4 x -1 y8
c)
a6
a7
-3
Unit 7 Review
3) Simplify using positive exponents.
a) (x-2y-4)-3(y7y3) = x6y12y10 = x6y22
b)
(2x5)3
=
4x-1y8
c)
a6
a7
-3
=
a-18
a-21
8x15x
4y8
=
a21
a18
=
=
2x16
y8
a3
Unit 7 Review
4) Write an exponential function to model each
situation (for x years). Find each amount after
the specified time.
a) $200 principal
5 years
4% compounded annually
b) $3000 investment
3 years
8% loss each year
Unit 7 Review
4) Write an exponential function to model each
situation (for x years). Find each amount after
the specified time.
a) $200 principal
y = 200·1.04x = $243.33
5 years
4% compounded annually
b) $3000 investment y = 3000·0.92x = $2336.06
3 years
8% loss each year
Unit 7 Review
Graph A
20
18
16
14
12
10
y
These graphs show functions
in the form y = a(b)x.
a. Which graph has b < 1?
8
6
4
2
0
b.
Which axis is an
asymptote in Graph B?
-6
-4
-2
0
2
4
x
Graph B
25
20
c.
What is the value of a in
Graph A?
15
y
5)
10
5
0
-2
-1
0
1
x
2
3
4
Unit 7 Review
5)
These graphs show functions
in the form y = a(b)x.
a. Which graph has b < 1?
Graph B
b.
Which axis is an
asymptote in Graph B?
x-axis
c.
What is the value of a in
Graph A?
a=2
Unit 7 Review
Decay of Something
6) a) What is the
half life of this
substance?
110
100
90
80
g
70
60
50
b) Estimate an
exponential
equation that
models the graph.
40
30
20
10
0
0
10
20
30
40
50
minutes
60
70
80
90
100
Unit 7 Review
Decay of Something
6) a) What is the
half life of this
substance?
110
100
90
80
≈ 20 minutes
g
70
60
50
b) Estimate an
exponential
equation that
models the graph.
y = 100·bx  50 = 100·b20
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
minutes
y = 100·0.966x
 0.5 = b20  b = 20th root of 0.5  b ≈ 0.966