Nigeria's population grew from 95.3 million (1990) to 122.4 million (2000) — an increase of about 28.4% over one decade.
A student says: "The population grew 2.84% per year because 28.4% ÷ 10 = 2.84%."
Is this correct? Use this organizer to explain why or why not.
Word Bank
adds
multiplies
same amount
same factor
divide
take the 10th root
linear
exponential
Compare: Linear vs. Exponential Growth
| Linear Growth |
Exponential Growth |
| Each year, the population the same . |
Each year, the population by the same . |
| To find the yearly rate, you can by 10 because the growth is spread evenly. |
To find the yearly rate, you must because the growth compounds each year. |
| Nigeria's growth is / is not (circle one) this type. |
Nigeria's growth is / is not (circle one) this type. |
Conclusion — Complete Using the Word Bank
Try Writing
"28.4% ÷ 10 = 2.84% is incorrect because Nigeria's population growth is
growth, not
growth.
To find the annual growth factor, I need to
of 1.284."
Page 1 of 3 · Unit 5 · Lesson 4 Graphic Organizers (Level 1–2)
Cesium-137 has a half-life of 30 years. Starting with 100 grams, the amount remaining is given by:
100 · (½)n where n is the number of 30-year periods.
How to fill in the table: The exponent tells you how many 30-year periods have passed.
Multiply the exponent by 30 to get the total years.
Example: exponent = 3 → 3 periods → 3 × 30 = 90 years
Fill in the table — the expression column is done for you
| Expression |
Exponent (n) |
# of 30-year periods |
Total years |
| 100 · (½)1 |
1 |
|
|
| 100 · (½)3 |
3 |
|
|
| 100 · (½)1/30 |
1/30 |
|
|
| 100 · (½)1/2 |
1/2 |
|
|
Sentence Frame — Choose one row and explain it
Try Writing
"The exponent means
30-year period(s),
which is years."
Page 2 of 3 · Unit 5 · Lesson 4 Graphic Organizers (Level 1–2)
Part 1 — Match each term to its definition
Terms
1.
half-life
(letter: ___)
2.
initial amount
(letter: ___)
3.
exponent
(letter: ___)
4.
root
(letter: ___)
Definitions
- A. The starting quantity before any decay has occurred — 200 mg in the cool-down.
- B. The power that a base is raised to; tells you the number of intervals.
- C. The time it takes for half of a material to remain.
- D. The inverse of raising to a power; used to find a subinterval factor, the decay (or growth) over a smaller time period than the one you were given.
Part 2 — Use two vocabulary terms to complete the sentence frame
A(t) = 200 · (½)t/8 describes the amount of Iodine-131 remaining, where t is days.
Try Writing
If t = 8 days, the exponent equals 8 ÷ 8 = . That means half-life has passed.
If t = 16 days, the exponent equals 16 ÷ 8 = . That means half-lives have passed.
Part 3 — Circle which type of growth this is
Linear Growth
(adds the same amount each period)
Exponential Growth
(multiplies by the same factor each period)
Page 3 of 3 · Unit 5 · Lesson 4 Graphic Organizers (Level 1–2) · Note: Cool-Down Level 1–2 scaffold is in unit5_lesson4_cooldown_materials.html (Page 2)