MHR • Advanced Functions 12 Solutions 660

Chapter 7 Section 2 Question 17 Page 377
Solutions to Achievement Check questions are provided in the Teacher’s Resource.
Chapter 7 Section 2 Question 18 Page 377
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a) If A 0 is the initial amount, y = A 0
! A 0
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t
20
b) Time starts at 0 s and continues forever. The amount starts at 0 g and continues until all the
platinum-197 is gold-197.
Domain: {t ∈ R, t ≥ 0}; Range: {y ∈ R, 0 < y ≤ A 0 }
Chapter 7 Section 2 Question 19 Page 377
Answers may vary. A sample solution is shown.
a) The carbon fusion cycle takes place in very hot stars. During the cycle, the addition of four
hydrogen atoms changes a carbon atom into other elements before returning it back to carbon
and releasing a helium atom and two positrons. At each of the six stages of the process,
energy is released.
Every time a carbon cycle takes place, two of the four protons are destroyed.
b) Call the protons in hydrogen and helium atoms available protons. If there are 5 × 10 13
available protons in a star, how many will there be after three complete carbon cycles?
Solution: 5 × 10 13 (0.5) 3 = 6.25 × 10 12
After how many carbon cycles will there be fewer than 10% of the original available protons?
Solution: Find when 0.5 x is less than 0.1: (0.5) 3 = 0.125 and (0.5) 4 = 0.0625
After four complete carbon cycles.
MHR • Advanced Functions 12 Solutions 690