MATH 1090 Algebra and Trigonometry
Problem Set 6 - Questions
2002 Winter
Sketch the graphs of
y = 3x -
1
y = 3x
- 1
y = 1 -
3-x
Evaluate, without using a calculator,
log420 -
log45
eln 5 + 2 ln 3
Simplify for general x > -1
and evaluate for x = 1 :
Write down the domain and range of
f (x) = ln (x + 3)2
f (x) = 2 ln (x + 3)
Express the solution set to these equations in terms of natural
logarithms (or e) and, where necessary, use a calculator to
obtain a decimal approximation, correct to three decimal places, for
the solution.
10x = 17.65
e4x - 5
- 7 = 11 243
3x/7 = 0.2
e4x -
3 e2x - 18 = 0
log2(x - 1)
+ log2(x + 1) = 3
log2(4x + 1) = 5
The number n(t) of radioactive atoms
remaining at time t is
where no = n(0) is the initial
number of radioactive atoms at time t = 0
and
h is the half-life.
In each interval of one half-life, half of all remaining radioactive
atoms decay.
What proportion of the radioactive atoms remains after six
half-lives?
How many half-lives does it take before less than one-millionth of
the original number of radioactive atoms remains?
[Challenge question:]
The exponential decay law can also be expressed as
n(t) = noe-kt
Find k in terms of h.
Also: Try the questions from exercise sets 4.1 to 4.5
of the textbook.
The solutions to this problem set will
appear elsewhere on this web site.