1. Algebra I Chapter 8 Review

2. 1) A population of bacteria triples in size every 5 hours.
Chapter 8 Review
1) A population of bacteria triples in size every 5 hours.
If the initial population of the bacteria is 125 cells, what will the population be after 15 hours?
If the initial population of the bacteria is 125 cells, what will the population be after 25 hours?
Model the bacteria population with an exponential function.

3. Answer 1) A population of bacteria triples in size every 5 hours.
Chapter 8 Review
1) A population of bacteria triples in size every 5 hours.
If the initial population of the bacteria is 125 cells, what will the population be after 15 hours?
If the initial population of the bacteria is 125 cells, what will the population be after 25 hours?
Model the bacteria population with an exponential function.
3,375 cells
30,375 cells
y = 125 · 3x
where x is the number of 5 hour cycles

4. 2) Write each in scientific notation. 34,000,000 0.00063 123.456
Chapter 8 Review
2) Write each in scientific notation.
34,000,000

5. 2) Write each in scientific notation. 34,000,000 0.00063 123.456
Answer
Chapter 8 Review
2) Write each in scientific notation.
34,000,000
= 3.4  107
= 6.3  10-4
=  102

6. 3) Write each in standard notation. 8.05  106 4.25  10-4
Chapter 8 Review
3) Write each in standard notation.
8.05  106
4.25  10-4

7. 3) Write each in standard notation. 8.05  106 4.25  10-4
Answer
Chapter 8 Review
3) Write each in standard notation.
8.05  106
4.25  10-4
= 8,050,000 =

8. 3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3 4x-1y8
Chapter 8 Review
3) Simplify using positive exponents.
(x-2y-4)-3(y7y3)
(2x5)3
4x-1y8
a6 -3 a7

9. Answer 3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3
Chapter 8 Review
3) Simplify using positive exponents.
(x-2y-4)-3(y7y3)
(2x5)3
4x-1y8
a6 -3 a7
= x6y12y10 = x6y22
8x15x x16
= =
4y y8
a a a3
= = =
a a18

10. Chapter 8 Review
4) Write an exponential function to model each situation (for x years). Find each amount after the specified time.
$200 principal
5 years
4% compounded annually
$3000 investment
3 years
8% loss each year

11. Answer
Chapter 8 Review
4) Write an exponential function to model each situation (for x years). Find each amount after the specified time.
$200 principal
5 years
4% compounded annually
$3000 investment
3 years
8% loss each year
y = 200·1.04x = $243.33
y = 3000·0.92x = $

12. 5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x
Chapter 8 Review
5) Graph. Label each growth or decay.
y = 2 · 3x
f(x) = 4 · (0.2)x

13. 5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x
Answer
Chapter 8 Review
5) Graph. Label each growth or decay.
y = 2 · 3x
f(x) = 4 · (0.2)x
growth
decay

14. Chapter 8 Review
a) What is the half life of this substance?
b) Estimate an exponential equation that models the graph.

15. Answer Chapter 8 Review a) What is the half life of this substance?
b) Estimate an exponential equation that models the graph.
≈ 20 minutes
y = 100·0.966x
y = 100·bx  50 = 100·b20
 0.5 = b20  b = 20th root of 0.5  b ≈ 0.966