Algebra II
Name: -~~P~b=--------Exponential Growth and Decay
The exponential models describe the population of the indicated country, A, in millions, t years after 2006. Use
these models to solve Exercises 1-6.
India -
Jet)
Iraq - Jet)
= 1095.4eo.o14t
Japan - JCt) = 127.5eo.oOlt
=
Russia - Jet)
26.8eo.027t
=
142.ge-o.o04t
1. What was the population of Japan in 2006?
2. What was the population of Iraq in 2006?
3. Which country has the greatest growth rate? By what percentage is the population of that country increasing
each year?
) ct. J 'J.
4. Which country has decreasing population? By what percentage is the population of that country decreasing
each year?
5. When will India's population be 1238 million?
6. When will India's population be 1416 million?
7. The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams ofkrypton-91 are initially
present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?
Ao ~ \lc
y~G.~
~~
\C)~O~c\S
~lLiC)')
~ l~O)~ ~ 5ilA~:)
~ loo') .~d 3\O-;'(VLS
~lso')
~ \
~'\0J0I'-
~ ~
51ON'fY\-
8. A bird species in danger of extinction has a population that is decreasing exponentially
(j(t)=Aoll). Five
years ago the population was at 1400 and today only 1000 of the birds are alive. Once the population drops
*
below 100, the situation will be irreversible.
At) -=~ ls)~
\ liDO
\()OO ~
--:t>
~
When will this happen?
It') ~ \L100~
- . DUll- .t:
,'=-
\ DO -::::.\ 4 DO E--
l ~J~ \liDO EE1<-
'\~ ~ -.l) lo~ \
9. the growth model
fCt) =
107.4eo,Olt describes New Zealand's
2006.
a) What is New Zealand's
growth rate?
b) How long will it take New Zealand to double its population?
population,f(t)
in millions,
t years after