have you ever wondered how many people might inhabit the us in 20 years?
DESCRIPTION
Have you ever wondered how many people might inhabit the US in 20 years?. For example, if the US population grows by 1.5% each year, how many people will there be in 20 years?. In this lesson you will learn how to create and graph exponential relationships by using exponential functions. - PowerPoint PPT PresentationTRANSCRIPT
Have you ever wondered how many people might inhabit the US in 20
years?For example, if the US population grows by 1.5% each year, how many people
will there be in 20 years?
In this lesson you will learn how to create and graph
exponential relationships by using exponential functions
Let’s Review
Example: You start with 25 dots, and the number of dots increase by 40% in
every step.
40% growth 40% growth
Let’s Review
40% growth 40% growth
y = a(1+r)x
y = 25(1+.4)x
y = 25(1.4)x
Let’s Review
Exponential growth
Exponential decay
A Common Mistake
If the values are growing, the growth factor is greater than 1
y = 25(1.4)x
If it is decaying, the decay factor is less than 1 but more than 0
y = 25(.4)x
Core Lesson
We will investigate the following:The population of the United States has
grown by approximately 1.5% each year for the past 100 years. If the population of the US was 92.2 million 100 years ago, create
and graph the function relating time and the population of the US.
Core Lesson
p = a(1+r)t
p = (92.2)*(1+r)t
p = (92.2)*(1+.015)t
p = (92.2)*1.015t
92.2 (million) start pop.
1.5% growth every year
Core Lesson
time (years)
pop
ula
tion
(millio
ns)
Input (t) Output (p)
0 92.2
10 107
20 124
30 144
40 167
50 194
75 281
100 408
p = (92.2)*1.015t
050
100150200250300350400450
0 50 100
In this lesson you have learned how to create and graph
exponential relationships by using exponential functions
Guided Practice
We will investigate the following:During the 19th century, American settlers
hunted bison almost to extinction. If 15% of the population was killed each year, and they
started with an initial population of 1,000,000, create and graph the relationship
between time and number of bison remaining.
Guided Practice p = a(1+r)t
p = (1000)*(1+r)t
p = (1000)*(1-.15)t
p = (1000)*0.85t
1000 (thousands) start pop.
15% decay every year
Guided Practice
time (years)
pop
ula
tion
(thou
san
ds)
Input (t) Output (p)
0 1000
5 443
10 197
15 87
20 39
25 17
30 7.6
50 .29
p = (1000)*0.85t
0
200
400
600
800
1000
1200
0 20 40 60
Extension Activities
1. Explore what effect changing the growth/decay factor has on a populations growth/decay.
2. Your bank account may have a “compounded interest”. Investigate compound interest and relate it to exponential functions.
3. Investigate the population of the world over the past 4000 years. Can the population be modeled with an exponential function. Justify your answer.
Quick Quiz
1. A population of bacteria will grow by about 20% each hour. If a colony of bacteria start with 2000, create and graph the relationship between time and colony size.
2. A certain new car’s value is said to “depreciate” (lose value exponentially) at a rate of 12% each year. If the car was originally priced at $28,000, create and graph the relationship between time and the car’s value.