Unit 3 Day 4: Exponential Relations
Description
Exponential Relations in Real World Applications
Discussion
A function of the form y = ax, where a > 0 and a ≠ 0, is the
exponential function. Such functions have a y-intercept 1, and no
x-intercept.
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Key Concept
Exponential growth or decay can be modelled using an
exponential function of the form y = kax , where k is the initial
amount, a is the change factor, and x is the number of changes
over a given time.
Home Activity or Further Classroom Consolidation
Students complete Part D of BLM 7.7.1
MBF 3C
MBF3C
BLM 7.7.1
Name:
Date:
Exponential Decay
1. The price of a new car is $24.599. Its value depreciates by 30% each
year. What is the depreciated value of the car after 4 years?
2. The hydrogen isotope tritium is radioactive, with a half-life of 12.5
years. A sample contains 35.2 units of radioactive tritium. What
amount would remain after 25 years?
3. In Canada the population of children in the age group 0–14 years has
been declining by 0.7% per year. The population of this age group in
1999 was about 5 917 000, Write an exponential function to model
this population decline.
4. The population of Newfoundland has been decreasing at an annual
rate of 0.8%. The population in 1999 was about 541 000.
a. Write an exponential function to model the population decrease
of Newfoundland.
b. Use the exponential function to predict the population of
Newfoundland in the year 2025.
Solutions: 1. 5906.22
2. 8.8
3. 5917000(1-0.007)x
4. a) 541000(1-0.008) x b) 439037
MBF3C
BLM 7.8.1
Name:
Date:
Cats and Mice!
There is an isolated island off the West coast of Canada. The island has
become overrun with mice, so the Wildlife Federation of Canada released a
cat population on the island to stabilize the mouse population. In 1999, the
population of the mice was 23,576 and began to decrease at a rate of 2.5%
per year. In the same year, the population of cats was at 15,786 and was
increasing at a rate of 1.8% per year. Assume that there is no outside factor,
and that these rates continue in order to answer the following questions.
1. Create a table of values for each population. Find AND analyze the
first-differences. What can you say about the populationgrowth/decay?
Yr
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Pop.
23 576
22987
22412
21852
21305
20773
20253
19747
19253
18772
18303
Mice
1st
Yr.
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Pop.
15 786
16070
16359
16654
16954
17259
17569
17886
18208
18535
18869
Cats
1st
2. Create an exponential function that describes the population of the
mice AND create an exponential function that describes the
population of the cats. How did you come up with this equation?
3. On the graphing calculator, plot the function that represents the
population of the mice AND the function that represents the
population of the cats.
4. How do the populations differ? How are they connected?
5. When would the population of the cats be greater than the population
of the mice?
6. When would the populations be the same? How can you tell?
7. What will happen to both the mice and cats populations if this trend
continues?
8. Write a brief paragraph summarizing your findings regarding the mice
and cats populations.
MBF3C
BLM 7.8.2
Evaluate:
1. 46÷43=
4. 45x4-2
7. (24)2
10. 38÷35
Name:
Date:
Exponential Relations
2. 160
5. (32)3
8. 58÷54
11. 5-3
3. 11-1
6. 25
9. 52x52
12. (43)2
Identify each of the following equations as either linear, exponential or
quadratic.
13. y = 3x
14. y = 3x
15. y = 3x2
16. y = -0.75x
17. y = -0.75x
18. y = -0.75x2 + 2
19. y = x2 + 5
20. y = 16x
For each exponential situation, identify its characteristics:
21. A club uses email to contact its members. The chain starts with 3
members who each contact three more members. Then those
members (9) each contact 3 members, and so the contacts continue.
22. A bouncing ball rebounds to 0.75 of its height on each bounce. The
ball was dropped from a height of 30 metres.
23. A painting was bought for $475. Each year, its value increases by
8%.