MBF3C
Unit 4 - Exponents
Exponential Decay
1) As of 1999, the deer population in Algonquin National Park has been declining. The decline can be
modeled by the equation P  846(0.986) t , where P is population, and t is the number of years since
1999.
a)
b)
c)
d)
How many deer where there in Algonquin Park in 1999?
How many deer are there in the park now?
How many will there be in 2015?
At what rate is the deer population declining?
[846; 756; 675; 1.4%]
2) The number of cod caught of the coast of Newfoundland is declining at a rate of 12% annually.
Only 20,000 tons of cod were caught last year.
a) Write an equation to model the decline of the cod population.
b) How any tons of cod will be caught this year?
c) How many tons will be caught in 2017?
[ P  20,000(1  0.12) 2 ; 19,600; 16,074]
3) Uranium-235 (U-235) is used in CANDU nuclear reactors, such as the ones that provide electricity
to large portions of Ontario. A typical CANDU reactor fuel rod contains about 50 kg of U-235. U235 has a half-live of 704 million years.
a) Write an equation to model the decay of U-235.
b) How much U-235 will be left in the fuel rod by the time you’re 50?
c) How much U-235 will be left in the rod in the year 2222?
x
1
[ y  50  ; 49.99999998 kg; 49.99998942 kg]
2
4) Industrial radiologists use Iridium-192 (Ir-192) to take X-rays of welds to ensure tat meet safety
standards. The half-life of Ir-192 is only 74 days. If an industrial radiologist uses a sample of Ir-192
that weighs 45g, how much of it will be left after a year?
[1.48g]
5) One part per trillion (ppt) of all living things is Carbon-14 (C-14). That concentration remains
constant until they die. Upon their death, the concentration starts to decay exponentially. C-14 has a
half-life of 5370 years. If an animal bone from 900 AD is carbon-dated, what concentration of C-14
will it have?
[0.87 ppt]
6) Cobalt-60 (Co-60) is used to sterilize medical equipment. It has a half-life of 5.24 years. If after
1.69 years, there’s only 80 g left of a sample of Co-60, how large was the sample to being with?
[100 g]
Page 401: # 2 (b,c), 3(a)
Page 410: # 2-5, 7